We describe a first-order theory of generalized sets intended to allow a similar treatment of sets and proper classes. The theory is motivated by the iterative conception of set. It has a ternary membership symbol interpreted as membership relative to a set-building step. Set and proper class are defined notions. We prove that sets and proper classes with a defined membership form an inner model of Bernays-Morse class theory. We extend ordinal and cardinal notions to (...) generalized sets and prove ordinal and cardinal results in the theory. We prove that the theory is consistent relative to ZFC + (∃ x) [ x is a strongly inaccessible cardinal]. (shrink)

We propose certain clases that seem unable to form a completed totality though they are very small, finite, in fact. We suggest that the existence of such clases lends support to an interpretation of the existence of proper clases in terms of availability, not size.

We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate ($\models^*$) appropriate to such structures. We indicate the utility of this theory as a framework for the development of the metatheory of first-order predicate logic and set theory, and we use it to prove that for any recursively enumerable extension $\Theta$ of ZF there is a finitely axiomatizable extension $\Theta'$ of GB that is a conservative extension of $\Theta$. (...) We also prove a conservative extension result that justifies the use of $\models^*$ to characterize ground models for forcing constructions. (shrink)

In this paper the authors argue that if Tarski’s definition of truth for the calculus of classes is correct, then set theories which assert the existence of proper classes (classes which are not the member of anything) are incorrect.

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF (...) of the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

Clark and Krauss [1977] presents a classification of complete, satisfiable and o-categorical theories in first order languages with finite non-logical vocabularies. In 1988 the first author modified this classification and raised three questions about the distribution of finitely axiomatizable theories. This paper answers two of those questions.

We study properties of certain subclasses of the Dedekind finite sets in set theory without the axiom of choice with respect to the comparability of their elements and to the boundedness of such classes, and we answer related open problems from Herrlich’s “The Finite and the Infinite.” The main results are as follows: 1. It is relatively consistent with ZF that the class of all finite sets is not the only finiteness class such that any two of its elements (...) are comparable. 2. The principle “Small Violations of Choice” —introduced by A. Blass—implies that the class of all Dedekind finite sets is bounded above. 3. “The class of all Dedekind finite sets is bounded above” is true in every permutation model of ZFA in which the class of atoms is a set, and in every symmetric model of ZF. 4. There exists a model of ZFA set theory in which the class of all atoms is a proper class and in which the class of all infinite Dedekind finite sets is not bounded above. 5. There exists a model of ZF in which the class of all infinite Dedekind finite sets is not bounded above. (shrink)

I will discuss a variety of cases such that the subject's believing truly is somewhat of an accident, but less so than in a Gettier case. In each case, this is because her reasons are not ultimately undefeated full stop, but they are ultimately undefeated with certain qualifications. For example, the subject's reasons might be ultimately defeated considered in themselves but ultimately undefeated considered as a proper part of an inference to the best explanation that is undefeated without qualification. (...) In each section of the paper, I consider different qualifications and show how in each case we get an epistemic standing I call “coach-class knowledge”. First-class knowledge requires justifying reasons that are undefeated without qualification. Coach-class knowledge only requires qualified lack of defeat. I will use this distinction to bring debates over knowledge from falsehood and fake barns to an ecumenical resolution. In both cases, the subject enjoys coach-class rather than first-class knowledge. I will also show that the defeasible reasoning tradition can better account for graded accidental truth than safety theories. (shrink)

In this paper, we study the forcing axiom for the class of proper forcing notions which do not add ω sequence of ordinals. We study the relationship between this forcing axiom and many cardinal invariants. We use typical iterated forcing with large cardinals and analyse certain property being preserved in this process. Lastly, we apply the results to distinguish several forcing axioms.

De Finetti introduced the concept of coherent previsions and conditional previsions through a gambling argument and through a parallel argument based on a quadratic scoring rule. He shows that the two arguments lead to the same concept of coherence. When dealing with events only, there is a rich class of scoring rules which might be used in place of the quadratic scoring rule. We give conditions under which a general strictly proper scoring rule can replace the quadratic scoring rule (...) while preserving the equivalence of de Finetti’s two arguments. In proving our results, we present a strengthening of the usual minimax theorem. We also present generalizations of de Finetti’s fundamental theorem of prevision to deal with conditional previsions. (shrink)

Let Q be an equivalence relation whose equivalence classes, denoted Q[x], may be proper classes. A function L defined on Field(Q) is a labelling for Q if and only if for all x,L(x) is a set and L is a labelling by subsets for Q if and only if BG denotes Bernays-Gödel class-set theory with neither the axiom of foundation, AF, nor the class axiom of choice, E. The following are relatively consistent with BG. (1) E is (...) true but there is an equivalence relation with no labelling.(2) E is true and every equivalence relation has a labelling, but there is an equivalence relation with no labelling by subsets. (shrink)

The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...) class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

For linear distribution classes, mean-variance and expected utility specifications have been shown in the literature to be fully compatible when studying the concepts of risk aversion, prudence, risk vulnerability and temperance. This paper shows that such compatibility does hold for the concept of standard risk aversion but not for the concepts of proper risk aversion and proper prudence.

In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ 1 -definable in (H(ω 2 ), ∈). Second, the Proper Forcing Axiom implies that the class of uncountable linear orders has a five element basis. The elements are X, ω 1 , ω 1 * , C, C * where X is any suborder of the (...) reals of size ω 1 and C is any Countryman line. Third, the Proper Forcing Axiom implies the Singular Cardinals Hypothesis at κ unless stationary subsets of S κ + ω reflect. The techniques are expected to be applicable to other open problems concerning the theory of H(ω 2 ). (shrink)

We show, assuming weak large cardinals, that in the context of games of length \ with moves coming from a proper class, clopen determinacy is strictly weaker than open determinacy. The proof amounts to an analysis of a certain level of L that exists under large cardinal assumptions weaker than an inaccessible. Our argument is sufficiently general to give a family of determinacy separation results applying in any setting where the universal class is sufficiently closed; e.g., in third, seventh, (...) or \\)th order arithmetic. We also prove bounds on the strength of Borel determinacy for proper class games. These results answer questions of Gitman and Hamkins. (shrink)

Assembly of minimal genomes revealed many genes encoding unknown functions. Three overlooked functional categories account for some of them. Cells are prone to make errors and age. As a first key function, discrimination between proper and changed entities is indispensable. Discrimination requires management of information, an authentic, yet abstract, cur- rency of reality. For example proteins age, sometimes very fast. The cell must identify, then get rid of old proteins without destroying young ones. Implementing discrimination in cells leads to (...) the second set of functions, usually ignored. Being abstract, information must nevertheless be embodied into material entities, with unavoidable idiosyncratic properties. This brings about novel unmet needs. Hence, the buildup of cells elicits specific but awkward material implementations, ‘kludges’ that become essential under particular settings, while difficult to identify. Finally, a third functional category char- acterizes the need for growth, with metabolic implementations allowing the cell to put together the growth of its cytoplasm, membranes, and genome, spanning different spatial dimensions. Solving this metabolic quandary, critical for engineering novel synthetic biology chassis, uncovered an unexpected role for CTP synthetase as the coordinator of nonhomothetic growth. Because a significant number of SynBio constructs aim at creating cell factories we expect that they will be attacked by viruses (it is not by chance that the function of the CRISPR system was identified in industrial settings). Substantiating the role of CTP, natural selection has dealt with this hurdle via synthesis of the antimetabolite 30-deoxy-30,40-didehydro- CTP, recruited for antiviral immunity in all domains of life. (shrink)

We prove two general results about the preservation of extendible and $C^{(n)}$ -extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vopěnka’s Principle and $C^{(n)}$ -extendible cardinals under Jensen’s iteration for forcing the GCH [17], previously obtained in [8, 27], respectively. We prove that $C^{(n)}$ -extendible cardinals are preserved by forcing with standard Easton-support iterations for any possible $\Delta _2$ -definable behaviour of the power-set function on (...) regular cardinals. We show that one can force proper class-many disagreements between the universe and HOD with respect to the calculation of successors of regular cardinals, while preserving $C^{(n)}$ -extendible cardinals. We also show, assuming the GCH, that the class forcing iteration of Cummings–Foreman–Magidor for forcing $\diamondsuit _{\kappa ^+}^+$ at every $\kappa $ [10] preserves $C^{(n)}$ -extendible cardinals. We give an optimal result on the consistency of weak square principles and $C^{(n)}$ -extendible cardinals. In the last section prove another preservation result for $C^{(n)}$ -extendible cardinals under very general (not necessarily definable or weakly homogeneous) class forcing iterations. As applications we prove the consistency of $C^{(n)}$ -extendible cardinals with $\mathrm {{V}}=\mathrm {{HOD}}$, and also with $\mathrm {GA}$ (the Ground Axiom) plus $\mathrm {V}\neq \mathrm {HOD}$, the latter being a strengthening of a result from [14]. (shrink)

In transfinite arithmetic 2n is defined as the cardinality of the family of all subsets of some set v with cardinality n. However, in the arithmetic of recursive equivalence types 2N is defined as the RET of the family of all finite subsets of some set v of nonnegative integers with RET N. Suppose v is a nonempty set. S is a class over v, if S consists of finite subsets of v and has v as its union. Such a (...) class is an intersecting class over v, if every two members of S have a nonempty intersection. An IC over v is called a maximal IC , if it is not properly included in any IC over v. It is known and readily proved that every MIC over a finite set v of cardinality n ≥ 1 has cardinality 2n-1. In order to generalize this result we introduce the notion of an ω-MIC over v. This is an effective analogue ot the notion of an MIC over v such that a class over a finite set v is an ω-MIC iff it is an MIC. We then prove that every ω-MIC over an isolated set v of RET N ≥ 1 has RET 2N-1. This is a generalization, for while there only are χ0 finite sets, there are ϰ isolated sets, where c denotes the cardinality of the continuum, namely all the finite sets and the c immune sets. MSC: 03D50. (shrink)

In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary gradient, spoiling Gauss's law. The secondary first-class constraint p^i,_i=0 still holds, but being a function of derivatives of momenta, it is not directly about E. Only a special combination of the two first-class constraints, the Anderson-Bergmann -Castellani gauge generator G, leaves E (...) unchanged. This problem is avoided if one uses a first-class constraint as the generator of a _canonical transformation_; but that partly strips the canonical coordinates of physical meaning as electromagnetic potentials and makes the electric field depend on the smearing function, bad behavior illustrating the wisdom of the Anderson-Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation dot{q}- dH/dp= -E_i -p^i=0 supports using the primary Hamiltonian rather than the extended Hamiltonian. The results extend the Lagrangian-oriented reforms of Castellani, Sugano, Pons, Salisbury, Shepley, _etc._ by showing the inequivalence of the extended Hamiltonian to the primary Hamiltonian even for _observables_, properly construed in the sense implying empirical equivalence. Dirac and others have noticed the arbitrary velocities multiplying the primary constraints outside the canonical Hamiltonian while apparently overlooking the corresponding arbitrary coordinates multiplying the secondary constraints _inside_ the canonical Hamiltonian, and so wrongly ascribed the gauge quality to the primaries alone, not the primary-secondary team G. Hence the Dirac conjecture about secondary first-class constraints rests upon a false presupposition. The usual concept of Dirac observables should also be modified to employ the gauge generator G, not the first-class constraints separately, so that the Hamiltonian observables become equivalent to the Lagrangian ones such as the electromagnetic field F. (shrink)

According to proponents of the continuity hypothesis, metaphors represent one end of a spectrum of linguistic phenomena, which includes various forms of loosening/broadening, such as category extensions and approximations, as well as hyperbolic interpretations. The continuity hypothesis is used to establish that the inferences derived from the set of linguistic expressions mentioned above result from the same or nearly similar pragmatic processes. In this paper, we want to challenge that particular aspect of the continuity hypothesis. We do so based on (...) considerations and analysis of an understudied linguistic phenomenon that we call the metaphorical uses of proper names (MPNs). We first explain how MPNs represent a unique linguistic class distinguishable from, for example, nicknames. In addition, we offer some remarks on how MPNs can be understood against the background of current debates between referentialists and predicativists about names. Our discussion leads us to conclude that MPNs are categorically different from literal interpretations of proper names. We spell out the consequences that the results of our analysis have for the continuity hypothesis. (shrink)

The article traces the framing of Muslim Europeans as the continent’s Other by focusing on the silencing of queer Muslims within public debates around ‘Islam and homosexuality’. Ignoring class as a factor in the violence produced by the gentrification of urban spaces, the pitting of the gay community against the Muslim community posits the latter as a threat to the continent’s foundations that needs to be contained through forms of spatial governance in line with the neoliberal restructuring of the city. (...) Maintaining that this is a Europe-wide phenomenon, the article looks at Amsterdam as exemplifying the European metropole as a site of pseudo-homophile Islamophobia. Simultaneously, with activist groups like the queer of color collective Strange Fruit, it is also representative of the strategies of resistance developed by groups whose presence is virtually erased through culture clash discourses, namely queer Muslims. The article argues that an intersectional queer of color activism, as practiced by Strange Fruit, and a queer of color critique building on it, allows to undermine binaries from the Muslim/european dichotomy to the normative coming out narrative, invariably positioning queers of color as ‘not properly gay’. (shrink)

Cenzer, D., R. Downey, C. Jockusch and R.A. Shore, Countable thin Π01 classes, Annals of Pure and Applied Logic 59 79–139. A Π01 class P {0, 1}ω is thin if every Π01 subclass of P is the intersection of P with some clopen set. Countable thin Π01 classes are constructed having arbitrary recursive Cantor- Bendixson rank. A thin Π01 class P is constructed with a unique nonisolated point A and furthermore A is of degree 0’. It is shown (...) that no set of degree ≥0” can be a member of any thin Π01 class. An r.e. degree d is constructed such that no set of degree d can be a member of any thin Π01 class. It is also shown that between any two distinct comparable r.e. degrees, there is a degree that contains a set which is of rank one in some thin Π01 class. It is shown that no maximal set can have rank one in any Π01 class, while there exist maximal sets of rank 2. The connection between Π01 classes, propositional theories and recursive Boolean algebras is explored, producing several corollaries to the results on Π01 classes. For example, call a recursive Boolean algebra thin if it has no proper nonprincipal recursive ideals. Then no thin recursive Boolean algebra can have a maximal ideal of degree ≥0”. (shrink)

We study various classes of maximality principles, \\), introduced by Hamkins :527–550, 2003), where \ defines a class of forcing posets and \ is an infinite cardinal. We explore the consistency strength and the relationship of \\) with various forcing axioms when \. In particular, we give a characterization of bounded forcing axioms for a class of forcings \ in terms of maximality principles MP\\) for \ formulas. A significant part of the paper is devoted to studying the principle (...) MP\\) where \ and \ defines the class of stationary set preserving forcings. We show that MP\\) has high consistency strength; on the other hand, if \ defines the class of proper forcings or semi-proper forcings, then by Hamkins, MP\\) is consistent relative to \. (shrink)

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information (...) for more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

Given an ideal $I$ , let $\mathbb{P}_{I}$ denote the forcing with $I$ -positive sets. We consider models of forcing axioms $MA(\Gamma)$ which also have a normal ideal $I$ with completeness $\omega_{2}$ such that $\mathbb{P}_{I}\in \Gamma$ . Using a bit more than a superhuge cardinal, we produce a model of PFA (proper forcing axiom) which has many ideals on $\omega_{2}$ whose associated forcings are proper; a similar phenomenon is also observed in the standard model of $MA^{+\omega_{1}}(\sigma\mbox{-closed})$ obtained from a (...) supercompact cardinal. Our model of PFA also exhibits weaker versions of ideal properties, which were shown by Foreman and Magidor to be inconsistent with PFA. Along the way, we also show (1) the diagonal reflection principle for internally club sets ( $\mathit{DRP}(IC_{\omega_{1}})$ ) introduced by the author in earlier work is equivalent to a natural weakening of “there is an ideal $I$ such that $\mathbb{P}_{I}$ is proper”; and (2) for many natural classes $\Gamma$ of posets, $MA^{+\omega_{1}}(\Gamma)$ is equivalent to an apparently stronger version which we call $MA^{+\operatorname{Diag}}(\Gamma)$. (shrink)

An integral subresiduated lattice ordered commutative monoid (or integral srl-monoid for short) is a pair \(({\textbf {A}},Q)\) where \({\textbf {A}}=(A,\wedge,\vee,\cdot,1)\) is a lattice ordered commutative monoid, 1 is the greatest element of the lattice \((A,\wedge,\vee )\) and _Q_ is a subalgebra of _A_ such that for each \(a,b\in A\) the set \(\{q \in Q: a \cdot q \le b\}\) has maximum, which will be denoted by \(a\rightarrow b\). The integral srl-monoids can be regarded as algebras \((A,\wedge,\vee,\cdot,\rightarrow,1)\) of type (2, 2, (...) 2, 2, 0). Furthermore, this class of algebras is a variety which properly contains the varieties of integral commutative residuated lattices and subresiduated lattices respectively. In this paper we study the quasivariety of \(\{\wedge,\cdot,\rightarrow,1\}\) -subreducts of integral srl-monoids, which will be denoted by \(\mathsf {SR^s}\). In particular, we show that \(\mathsf {SR^s}\) is a variety. We also characterize simple and subdirectly irreducible algebras of \(\mathsf {SR^s}\) respectively. Finally, through a Hilbert style system, we present a logic which has as algebraic semantics the variety \(\mathsf {SR^s}\) and we apply this result in order to present an expansion of the previous logic which has as algebraic semantics the variety of integral srl-monoids. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 31.3 (2001) 15-29 [Access article in PDF] Globality, Organization, Class Samuel Weber 1 Although one could hardly imagine a topic more far-ranging than "Theory, Globalization, and the Remains of the University," it can be argued that it does not range far enough. Or perhaps ranges too far. For the questions suggested by this concatenation of terms cannot be limited to the fate or future of "theory" in whatever (...) will remain of the "university" in a globalized world. And yet it is no doubt significant that "theory" leads the parade—significant but also perhaps part of the problem. For not just etymology links "theory" to notions such as detached contemplation, spectatorship, and appropriation through vision. The history and practice that have been associated with this term continue, even today, to be indebted to the dualist paradigm of an underlying subject—today reformulated as "agent" or "position"—confronting and comprehending an ob-ject. And yet, if we are still discussing "theory," here and today, it is by virtue of a series of texts that have persistently and powerfully questioned the subject-object paradigm that has dominated theoretical discourse at least since Descartes, and sought to elaborate alternatives to it. Those alternatives have almost always involved a reflection upon language as the medium of a practice that is no longer "theoretical" in the traditional sense, because it no longer works within the parameters of the subject-object model of cognition and truth. From Kierkegaard to Nietzsche, Benjamin, Heidegger, de Man, and Derrida, the subject-object model of cognition has been reinterpreted as an effect of the medium of language, a medium that articulates itself through the reading, writing, and repetition of texts, understood as concatenations of significance that both respond to and address an irreducible alterity.The "university" has always occupied an equivocal position with respect to this "linguistic" problematization of the subject-object model of cognition and truth: not only because "the university" as such has never existed—not at least as the singular universal implied by the definite article—but even more, because of the traditional claim of universities to serve as places where universally valid cognition is both transmitted and produced. In this sense, notions such as "the globalization of the university" simply continue the universalizing claims built into universities and promoted by them in order to justify their social existence and dependency.The very notion, or rather figure, implied in the notion of "globalization" tends to strengthen such universalism. Coming after the struggle between Communist and Capitalist camps in the Cold War, "Globalization" stresses that there is no place left on the "globe" where the capitalist system, its values, its power, and way of life can be contested. The "globe" is all there is, and despite its diversity, it is to have a single future, prolongation of the prevailing relation of forces. Globalization is thus the successor to the notion of "One World," itself a recent offshoot of the "universal history" that was the Enlightenment heir of the Christian eschatological narrative. [End Page 15]But the university has also been one of the few places in modern society where such universalizing and homogenizing tendencies have also been reflected, reworked, and criticized, if not resisted. Thus, if the names mentioned above have any credence at all in the English-speaking world, it is in large part by virtue of its universities, which have extended a certain hospitality to their writings. Like all hospitality, however, that of the universities has rarely been a neutral one. There, as elsewhere, writings are admitted as legitimate "objects" of study only under the double condition, first, of being linked to "proper names," and second, of being received and validated by existing disciplines. In short, writings are received for study in universities on the condition that they be certified as proper "theoretical objects" for "theoretical subjects" defined and validated through their appurtenance to the existing academic division of labor. This division of labor founds its disciplines in the subject-object model of cognition and of truth.This is why the hermeneutic and poststructuralist turn (back) to language as a signifying medium rather than... (shrink)

Helix–loop–helix (HLH) genes encode for transcription factors affecting a whole variety of developmental programs, including neurogenesis. At least seven functional classes (denoted I to VII) of HLH genes exist,1 with subclass members exhibiting homo‐ and heterodimerisation for proper DNA binding and transcriptional regulation of downstream target genes. In the developing nervous system, members of class II, V and VI have been most extensively studied concerning their roles in neural programming. In contrast, the function of class I proteins (such (...) as E12 and E47) is poorly defined and the orthodox view relegates them to general dimerisation duties that are necessary for the activity of the other classes. However, closer scrutiny of the spatiotemporal expression patterns of class I factors, combined with recent biochemical evidence, would suggest that class I proteins possess specific functions during early neural differentiation. This essay supports this possibility, in addition to putting forward the hypothesis that, outside their general dimerisation activity, class I genes have independent roles in regulating neurogenesis. BioEssays 25:709–716, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

Analyzing the effective content of the Lebesgue density theorem played a crucial role in some recent developments in algorithmic randomness, namely, the solutions of the ML-covering and ML-cupping problems. Two new classes of reals emerged from this inquiry: thepositive density pointswith respect toeffectively closed sets of reals, and a proper subclass, thedensity-one points. Bienvenu, Hölzl, Miller, and Nies have shown that the Martin-Löf random positive density points are exactly the ones that do not compute the halting problem. Treating (...) this theorem as our starting point, we present several new results that shed light on how density, randomness, and computational strength interact. (shrink)

For the classA of uncountable Archimedian real closed fields we show that the statement “TheL <ω-theory ofA is complete” is independent of ZFC. In particular we have the following results:Assuming the Continuum-Hypothesis (CH) is incomplete. Conversely it is possible to build a model of set theory in which is complete and decidable. The latter can also be deduced from the Proper Forcing Axiom (PFA). In this case turns out to be equivalent to the elementary theory of the real numbers (...) ℝ (by a quantifier-elimination procedure).Formally: is incomplete. is complete and decidable. (shrink)

A class K of structures is controlled if, for all cardinals λ, the relation of L ∞,λ-equivalence partitions K into a set of equivalence classes (as opposed to a proper class). We prove that the class of doubly transitive linear orders is controlled, while any pseudo-elementary class with the ω-independence property is not controlled.

Aboriginal fringe-dwellers in Central Australia emphasize their independence of the white-dominated world around them. Because of differences in their means of support, men and women have developed variations on this perspective of independence and personal power. Men present themselves in terms of their white employers and base their personal collateral on those links. Women stress their ability to care for their families without help from others and present themselves as able to play all social roles in the Central Australian world. (...) This image of woman as universal actor places moral premiums on the protection of domestic interests at the expense of wider gender, ethnic, or class interests. These ideas are explored through analysis of the life story of one woman, Katy Mayhew. Although obtained in an interview setting, the occasion of Katy's story became a life event through which she, her daughter, and her “sisters” reflected upon their lives as Aboriginal women in Central Australia. It is argued that life events are particularly appropriate ways for people to reflect on the meaning of their mundane, everyday lives in contexts such as Aboriginal Australia, which are dominated by bureaucratic frames, processes, and power. (shrink)

Bertrand Russell introduced several novel ideas in his 1903 Principles of Mathematics that he later gave up and never went back to in his subsequent work. Two of these are the related notions of denoting concepts and classes as many. In this paper we reconstruct each of these notions in the framework of conceptual realism and connect them through a logic of names that encompasses both proper and common names, and among the latter, complex as well as simple (...) common names. Names, proper or common, and simple or complex, occur as parts of quantifier phrases, which in conceptual realism stand for referential concepts, i.e., cognitive capacities that inform our speech and mental acts with a referential nature and account for the intentionality, or directedness, of those acts. In Russell’s theory, quantifier phrases express denoting concepts (which do not include proper names). In conceptual realism, names, as well as predicates, can be nominalized and allowed to occur as "singular terms", i.e., as arguments of predicates. Occurring as a singular term, a name denotes, if it denotes at all, a class as many, where, as in Russell’s theory, a class as many of one object is identical with that one object, and a class as many of more than one object is a plurality, i.e., a plural object that we call a group. Also, as in Russell’s theory, there is no empty class as many. When nominalized, proper names function as "singular terms" just the way they do in so-called free logic. Leśniewski’s ontology, which is also called a logic of names can be completely interpreted within this conceptualist framework, and the well-known oddities of Leśniewski’s system are shown not to be odd at all when his system is so interpreted. Finally, we show how the pluralities, or groups, of the logic of classes as many can be used as the semantic basis of plural reference and predication. We explain in this way Russell’s "fundamental doctrine upon which all rests", i.e., "the doctrine that the subject of a proposition may be plural, and that such plural subjects are what is meant by classes [as many] which have more than one term" (Russell 1938, p. 517). (shrink)

The stability theory of first order theories was initiated by Saharon Shelah in 1969. The classification of abstract elementary classes was initiated by Shelah, too. In several papers, he introduced non-forking relations. Later, Shelah [17, II] introduced the good non-forking frame, an axiomatization of the non-forking notion.We improve results of Shelah on good non-forking frames, mainly by weakening the stability hypothesis in several important theorems, replacing it by the almost λ-stability hypothesis: The number of types over a model of (...) cardinality λ is at most λ+.We present conditions on Kλ, that imply the existence of a model in Kλ+n for all n. We do this by providing sufficiently strong conditions on Kλ, that they are inherited by a properly chosen subclass of Kλ+. What are these conditions? We assume that there is a ‘non-forking’ relation which satisfies the properties of the non-forking relation on superstable first order theories. Note that here we deal with models of a fixed cardinality, λ.While in Shelah [17, II] we assume stability in λ, so we can use brimmed models, here we assume almost stability only, but we add an assumption: The conjugation property.In the context of elementary classes, the superstability assumption gives the existence of types with well-defined dimension and the ω-stability assumption gives the existence and uniqueness of models prime over sets. In our context, the local character assumption is an analog to superstability and the density of the class of uniqueness triples with respect to the relation ≼bs is the analog to ω-stability. (shrink)

After a decade in power, Venezuela’s Bolivarian Revolution faces a newly multilateral Washington DC and global capitalism’s most significant crisis in a generation. In order to properly understand the hopes and impediments for the future of the Revolution, I argue, it is first necessary to consider the current trajectory and series of accomplishments it has made. In this review-essay, I consider the three most recent and comprehensive works on the foreign and domestic situations in Venezuela in English ‐ Eva Golinger’s (...) Bush vs Chávez, Gregory Wilpert’s Changing Venezuela by Taking Power, and Steve Ellner’s Rethinking Venezuelan Politics. (shrink)

This article studies the extant class notes of a course on Descartes's Meditations on First Philosophy (1641) and (part of) the Principles of Philosophy (1644), which was given by the reformed theologian Christoph Wittich (1625–1687) at the former Dutch University of Nijmegen (1655–1679). This manuscript contains dictata, taken (presumably in 1664) under the title Observationes in Renati Descartes Meditationes de prima philosophia. Observations in ejusdem Principiorum philosophiae partem primam. This article mainly considers three themes surfacing in Wittich’s classes: (a) (...) doubt and scepticism; (b) “vulgar” and “proper philosophy”; (c) philosophy and Scripture. On the one hand, this study explains how Wittich tried to harmonise Cartesian metaphysics with his Calvinist faith by defining them as two autonomous fields of knowledge. On the other hand, Wittich’s ideas are shown to have met with much resistance on the part of some of his contemporary theologians. The study of Wittich’s course supplies new knowledge concerning the teaching of one of the first theologians to openly seek to combine Descartes's ideas and Copernican astronomy with the Bible. In so doing, this article offers direct insight into the way in which the new philosophy was taught in Nijmegen, and in the seventeenth-century Dutch Republic in general. (shrink)

We examine the differences between three standard classes of forcing notions relative to the way they collapse the continuum. It turns out that proper and semi-proper posets behave differently in that respect from the class of posets that preserve stationary subsets of \.

Though largely ignored by educators and researchers, boredom, an aversive emotion, is the hurdle for many translation learners to be professional. It is all the more important to unpack the boredom factors of Chinese foreign language major students in translation classes, which will serve in promoting students’ engagement in L2 classes and translator cultivation. By using a sequential mixed approach, this study conducted a thematic analysis and built a structural equation model. Quantitative data were gleaned from 483 foreign (...) major college students in China and qualitative data were selected from students of 7 universities through snowball sampling. Initially, the first-order confirmatory factor analysis verified the adapted questionnaire and the second-order CFA finds each factor’s contribution. Then, the thematic analysis gives support to the empirical findings. Both quantitative and qualitative analyses revealed that task-based boredom is the most routinely experienced boredom. Moreover, two major sources of boredom in translation classes are found, including task-based boredom and teacher-related boredom. It is suggested that teachers should improve their classes and use more interesting and engaging materials and tasks with the proper level of difficulty. The finding can help educators to identify the major boredom in the translation class and help potential professional translators to grow. Future studies will also be facilitated by the present study to find approaches to tackle these boredom sources. (shrink)

Learning to recognize visual objects from examples requires the ability to find meaningful patterns in spaces of very high dimensionality. We present a method for dimensionality reduction which effectively biases the learning system by combining multiple constraints via the use of class labels. The use of extensive class labels steers the resulting lowdimensional representation to become invariant to those directions of variation in the input space that are irrelevant to classification; this is done merely by making class labels independent of (...) these directions. We also show that prior knowledge of the proper dimensionality of the target representation can be imposed by training a multi-layer bottleneck network. Computational experiments involving non-trivial categorization of parameterized fractal images and of human faces indicate that the low-dimensional representation extracted by our method leads to improved generalization in the learned tasks and is likely to preserve the topology of the original space. (shrink)

Among Greek grammarians a distinction is recognized between a class of nouns capable of referring to several nouns and a class referring to just one proper name. This distinction is very poorly (and problematically) attested in the works of Latin grammarians. This paper explores and discusses some connections so far overlooked, and tries to correct some misinterpretations. In the light of the distinction of proper vs. common epithets, the controversial phrase mediae potestatis is elucidated, by stressing that it (...) refers to the ‘semantic incompleteness’ of the adjective. Finally, the assumption that the concept of ‘adjective’ was not known within Latin grammatical tradition before the fourth century is revised. We bring forward evidence against this assumption implying an early ‘linguistic’ tradition with respect to the adjective which was to some degree independent from the well-known ‘rhetorical’ doctrine on epithets. (shrink)

An enduring question in the cultural study of psychological experience concerns how emotion may play a role in shaping moral aspects of children’s lives as they are mentored into socially preferred ways of understanding and responding to the world at hand. This article brings together approaches from psychological and linguistic anthropology to explore how cultural schemas of normativity are communicated, embodied, and enacted as children participate in day-to-day family activities and routines. Illustrative examples emanate from a videotaped corpus of naturalistic (...) interactional data that document the daily lives of 32 ethnically diverse U.S. middle-class families who reside in the Los Angeles, California metropolitan region. The article employs discourse and narrative analysis to examine how children are apprenticed into perceiving, appraising, and reacting to the emotions of self and others as culturally shaped indicators for proper comportment. Data analysis emphasizes how implicit components of caregivers’ interactions with children (i.e., gesture, gaze, facial expression) intertwine with explicit, verbal communication to constitute intricately layered affective messages that shape the evaluative frames through which children interpret, display, and respond to emotions. The article identifies two culturally salient childrearing practices, “pep talks” and “time outs,” that apprentice children into moral accountable relationships with others by encouraging them to manage their emotions in culturally preferred ways. Study findings suggest that parental communications conveying praise and approval—or conversely indexing disapproval—towards children are emotionally resonant motivational practices in this cultural milieu as children are mentored into culturally meaningful emotional management techniques. The article highlights how children actively employ semiotic socio-communicative resources and it closely traces their sense-making processes in tandem with their discursive contributions to the moment-by-moment interaction. It argues that emotion, morality, and interpersonal relations are critical in shaping children’s acquisition of consensually validated ways of perceiving, feeling, and responding to the phenomena they encounter in their day-to-day lives. This perspective aims towards contextualized understandings that render plausible connections between local contexts of everyday action and broader macro-level discourses and master narratives, such as those associated with a neo-liberal emphasis on cultivating citizens who learn to regulate their emotions on behalf of self and others. (shrink)