Let M be an arbitrary structure. Then we say that an M -formula φ defines a stable set inM if every formula φ ∧ α is stable. We prove: If G is an M -definable group and every definable stable subset of G has U -rank at most n , then G has a maximal connected stable normal subgroup H such that G /H is purely unstable. The assumptions hold for example if M is interpretable in (...) an o-minimal structure.More generally, an M -definable set X is weakly stable if the M -induced structure on X is stable. We observe that, by results of Shelah, every weakly stable set in theories with NIP is stable. (shrink)

A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a relational semantics provided by structures based on polarities. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and (...) whose stable set lattices have additional operators that are first-order definable in the underlying structure. We show that such classes generate varieties of algebras that are closed under canonical extensions. The proof makes use of a relationship between canonical extensions and MacNeille completions. (shrink)

Two scenarios illustrate uses of von Neumann–Morgenstern stable sets in the construction of choice functions. A comparison is made to the construction of choice functions by the selection of maximal elements. A characterization is given of choice functions that are von Neumann–Morgenstern stable set rationalizable by acyclic, asymmetric binary relations. Two examples illustrate the use of the characterization.

This paper attempts to square libertarian principles with the reality of formal education by asking how far we should and can allow people to do as they wish in educational settings. The major focus is on children in schools, as the concept ‘childhood’ ipso facto implies restrictions on doing as one wishes, and schools as institutions entail inevitable constraints. Children by definition tend to enjoy stronger protection rights but weaker liberty rights than adults. A local preferential calculus is developed as (...) a guide for teachers, suggesting wishes should be granted where feasible and at least welfare neutral. In the case of teachers, employers set the parameters for the feasibility criterion but should also ensure at least welfare neutrality, while students in adult and higher education should be responsible for the feasibility and welfare outcomes of their own choices. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

Within Luo’s (2001, J. Math. Econ. 36, 95–109) framework of a general system, I establish an equivalence theorem for the conservative stable standard of behavior (CSSB for short) developed by J. Greenberg (“The Theory of Social Situation: An Alternative Game-Theoretic Approach,” Cambridge University Press, 1990). It is shown that a standard of behavior for a situation is a CSSB if, and only if, its graph is a φ-stable set for the associated general system.

The phenomenon whereby severely disabled persons self-report a higher than expected level of subjective well-being is called the “disability paradox.” One explanation for the paradox among brain injury survivors is “response shift,” an adjustment of one’s values, expectations, and perspective in the aftermath of a life-altering, disabling injury. The high level of subjective well-being appears paradoxical when viewed from the perspective of the non-disabled, who presume that those with severe disabilities experience a quality of life so poor that it might (...) make their lives not worth living. This presumption has profound consequences, for it may inform end-of-life choices made in advance directives, or influence decisions made by surrogates on behalf of persons who are unable to direct their own medical treatment. -/- Peterson et al propose a cautious, well-considered plan to use fMRI-based brain-computer interfaces to assess the decision making capacity of covertly aware, behaviorally non-responsive individuals who retain high levels of preserved cognition. Their plan, if it succeeds, could eventually restore autonomy and empower some severely disabled persons, allowing them to participate in clinical decision making. Peterson et al discuss possible in-principle objections to their proposal, among them the “argument from psychological health,” and the “changing sets of values” objection. These objections both presume that deviations from a pre-injury norm could indicate diminished decision making capacity. This presumption threatens the autonomy of the patient who is capable of making decisions, but whose post-injury decisions appear to diverge from pre-injury preferences or values. In light of the potential for response shift, and the disability paradox, it should not be inferred that changes in values or preferences are unreflective of the true current preferences of a brain-injured person, nor are they conclusive evidence of diminished capacity. Presuming diminished capacity on the basis of unexpected or unconventional preferences has, in the past, been used to disempower patients whose autonomy and capacity would not have been doubted had they made choices that accorded with the expectations or values of others. We must be cautious, and vigilant, to prevent similarly diminishing the autonomy of covertly aware, behaviorally non-responsive individuals on the basis of empirically and ethically questionable inferences about their decision making capacity. (shrink)

Gelfond and Lifschitz proposed the notion of a stable model of a logic program. We establish that the set of all stable models in a Herbrand universe of a recursive logic program is, up to recursive renaming, the set of all infinite paths of a recursive, countably branching tree, and conversely. As a consequence, the problem, given a recursive logic program, of determining whether it has at least one stable model, is Σ11-complete. Due to the equivalences established (...) in the authors' previous nonmonotone rule systems papers ), this applies equally to truth maintenance systems and default logics. (shrink)

The objective of this paper is to study stable coalition structures in symmetric majority games. We assume that players deviate from a coalition structure to another to maximize their power given by the Owen power index. We introduce three myopic core concepts and one farsighted stability concept, the farsighted vNM stable set. Our main result is that the pessimistic core, the largest myopic core, coincides with some farsighted vNM stable set for any number of players. Moreover, we (...) show that a coalition structure belongs to the pessimistic core and the farsighted vNM stable set if and only if it contains an exact majority coalition. (shrink)

For a many-to-many matching model with contracts, where all the agents have substitutable preferences, we provide an algorithm to compute the full set of stable allocations. This is based on the lattice structure of such set.

We study the behaviour of stable types in rosy theories. The main technical result is that a non-þ-forking extension of an unstable type is unstable. We apply this to show that a rosy group with a þ-generic stable type is stable. In the context of super-rosy theories of finite rank we conclude that non-trivial stable types of U þ -rank 1 must arise from definable stable sets.

In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are the formulas preserved in monotonic images (...) of frames and that ONNILLI-formulas are stable formulas as introduced by Bezhanishvili and Bezhanishvili in 2013. Thus, ONNILLI is a syntactically defined set of formulas axiomatizing all stable logics. This resolves a problem left open in 2013. (shrink)

The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are nonnull in a certain effective measure-theoretic sense. We show that the sets that can compute infinite homogeneous sets for nonnull many computable stable colorings and the sets that can compute infinite homogeneous sets for all computable (...) stable colorings agree below $\emptyset'$ but not in general. We also answer the analogs of two well-known questions about the stable Ramsey's theorem by showing that our weaker principle does not imply COH or WKL 0 in the context of reverse mathematics. (shrink)

We solve two problems from a work of Haskel and Pillay concerning maximal stable quotients of groups ∧-definable in NIP theories. The first result says that if G is a ∧-definable group in a distal theory, then Gst=G00 (where Gst is the smallest ∧-definable subgroup with G∕Gst stable, and G00 is the smallest ∧-definable subgroup of bounded index). In order to get it, we prove that distality is preserved under passing from T to the hyperimaginary expansion Theq. The (...) second result is an example of a group G definable in a nondistal NIP theory for which G=G00, but Gst is not an intersection of definable groups. Our example is a saturated extension of (R,+,[0,1]). Moreover, we make some observations on the question whether there is such an example which is a group of finite exponent. We also take the opportunity and give several characterizations of stability of hyperdefinable sets involving continuous logic. (shrink)

Recent work on formal theories of truth has revived an approach, due originally to Tarski, on which syntax and truth theories are sharply distinguished—‘disentangled’—from mathematical base theories. In this paper, we defend a novel philosophical constraint on disentangled theories. We argue that these theories must be epistemically stable: they must possess an intrinsic motivation justifying no strictly stronger theory. In a disentangled setting, even if the base and the syntax theory are individually stable, they may be jointly unstable. (...) We contend that this flaw afflicts many proposals discussed in the literature; we defend a new, stable disentangled theory, double second-order arithmetic. (shrink)

Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the (...) dimension function δ. In particular, the generic structure need not be ω-saturated and so the argument for stability is significantly more complicated. We further show that these structures are “flat” and do not interpret a group. (shrink)

For a NIP theory T, a sufficiently saturated model ${\mathfrak C}$ of T, and an invariant (over some small subset of ${\mathfrak C}$ ) global type p, we prove that there exists a finest relatively type-definable over a small set of parameters from ${\mathfrak C}$ equivalence relation on the set of realizations of p which has stable quotient. This is a counterpart for equivalence relations of the main result of [2] on the existence of maximal stable quotients of (...) type-definable groups in NIP theories. Our proof adapts the ideas of the proof of this result, working with relatively type-definable subsets of the group of automorphisms of the monster model as defined in [3]. (shrink)

A maximal almost disjoint (mad) family $\mathscr{A} \subseteq [\omega]^\omega$ is Cohen-stable if and only if it remains maximal in any Cohen generic extension. Otherwise it is Cohen-unstable. It is shown that a mad family, A, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the sets G[A], A ∈A are nowhere dense. An ℵ 0 -mad family, A, is a mad family with the property that given any countable family (...) $\mathscr{B} \subset [\omega]^\omega$ such that each element of B meets infinitely many elements of A in an infinite set there is an element of A meeting each element of B in an infinite set. It is shown that Cohen-stable mad families exist if and only if there exist ℵ 0 -mad families. Either of the conditions b = c or $\mathfrak{a} ) implies that there exist Cohen-stable mad families. Similar results are obtained for splitting families. For example, a splitting family, S, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the boundaries of the sets G[S], S ∈S are nowhere dense. Also, Cohen-stable splitting families of cardinality ≤ κ exist if and only if ℵ 0 -splitting families of cardinality ≤ κ exist. (shrink)

Action Languages are formal methods of talking about actions and their effects on fluents. One recent approach in planning is to define the domains of the planning problems using action languages. The aim of this research is to find a plan for a system defined in the action language C by translating it into a causal theory and then finding an equivalent logic program. The planning problem will then be reduced to finding the answer set (stable model) of this (...) logic program. This planner will be added as an extension to the Causal Calculator (CCALC) which is a model checker for the language of the causal theories. (shrink)

We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from 'primitive extensions' to the natural numbers a theory T μ of an (...) expansion of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable. (shrink)

This is a review of some of the definitions of the concept of a stable model that have been proposed in the literature. These definitions are equivalent to each other, at least when applied to traditional Prologstyle programs, but there are reasons why each of them is valuable and interesting. A new characterization of stable models can suggest an alternative picture of the intuitive meaning of logic programs; or it can lead to new algorithms for generating stable (...) models; or it can work better than others when we turn to generalizations of the traditional syntax that are important from the perspective of answer set programming; or it can be more convenient for use in proofs; or it can be interesting simply because it demonstrates a relationship between seemingly unrelated ideas. (shrink)

Vopenka [2] proved long ago that every set of ordinals is set-generic over HOD, Gödel's inner model of hereditarily ordinal-definable sets. Here we show that the entire universe V is class-generic over, and indeed over the even smaller inner model $\mathbb{S}=$, where S is the Stability predicate. We refer to the inner model $\mathbb{S}$ as the Stable Core of V. The predicate S has a simple definition which is more absolute than any definition of HOD; in particular, it (...) is possible to add reals which are not set-generic but preserve the Stable Core. (shrink)

We give some general criteria for the stable embeddedness of a definable set. We use these criteria to establish the stable embeddedness in algebraically closed valued fields of two definable sets: The set of balls of a given radius r < 1 contained in the valuation ring and the set of balls of a given multiplicative radius r < 1. We also show that in an algebraically closed valued field a 0-definable set is stably embedded if and (...) only if its algebraic closure is stably embedded. (shrink)

We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion ofseparation of quantifierswhich is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one functionμfrom ‘primitive extensions’ to the natural numbers a theoryTμof an expansion of an algebraically closed field which (...) has Morley rank 2. Finally, we show that ifμis not finite-to-one the theory may not beω-stable. (shrink)

An amalgamation base p in a simple theory is stably definable if its canonical base is interdefinable with the set of canonical parameters for the ϕ-definitions of p as ϕ ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably (...) definable amalgamation base whose restriction to the canonical base is not axiomatised by stable formulae are also given. The examples involve generic relations over non CM-trivial stable theories. (shrink)

We study how to partition a set of agents in a stable way when each coalition in the partition has to share a unit of a perfectly divisible good, and each agent has symmetric single-peaked preferences on the unit interval of his potential shares. A rule on the set of preference profiles consists of a partition function and a solution. Given a preference profile, a partition is selected and as many units of the good as the number of coalitions (...) in the partition are allocated, where each unit is shared among all agents belonging to the same coalition according to the solution. A rule is stable at a preference profile if no agent strictly prefers to leave his coalition to join another coalition and all members of the receiving coalition want to admit him. We show that the proportional solution and all sequential dictator solutions admit stable partition functions. We also show that stability is a strong requirement that becomes easily incompatible with other desirable properties like efficiency, strategy-proofness, anonymity, and non-envyness. (shrink)

We introduce a new class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising players are switching are always exceeded by the improvements in the payoffs of strategies which revising players are abandoning. We show that stable games subsume many well-known classes of examples, including zero-sum games, games with an interior ESS, wars of attrition, and concave potential games. We (...) prove that the set of Nash equilibria of any stable game is convex, and offer an elementary proof of existence of equilibrium. Finally, we show that the set of Nash equilibria of a stable game is globally asymptotically stable under a variety of evolutionary dynamics. These convergence results are proved by constructing Lyapunov functions defined in terms of revision potentials—that is, potential functions for the protocols agents follow when they consider switching strategies. (shrink)

We show that a formula φ(x, y) is stable if and only if φ is the pairing map on the unit ball of E x E * , where E is a reflexive Banach space. The result remains true if the formula φ is replaced by a set of formulas $p(\bar{x},\bar{y})$.

This doctoral dissertation investigates the notion of physical necessity. Specifically, it studies whether it is possible to account for non-accidental regularities without the standard assumption of a pre-existent set of governing laws. Thus, it takes side with the so called deflationist accounts of laws of nature, like the humean or the antirealist. The specific aim is to complement such accounts by providing a missing explanation of the appearance of physical necessity. In order to provide an explanation, I recur to fields (...) that have not been appealed to so far in discussions about the metaphysics of laws. Namely, I recur to complex systems’ theory, and to the foundations of statistical mechanics. The explanation proposed is inspired by how complex systems’ theory has elucidated the way patterns emerge, and by the probabilistic explanations of the 2nd law of thermodynamics. More specifically, this thesis studies how some constraints that make no direct reference to the dynamics can be a sufficient condition for obtaining in the long run, with high probability, stable regular behavior. I hope to show how certain metaphysical accounts of laws might benefit from the insights achieved in these other fields. According to the proposal studied in this thesis, some regularities are not accidental not in virtue of an underlying physical necessity. The non-accidental character of certain regular behavior is only due to its overwhelming stability. Thus, from this point of view the goal becomes to explain the stability of temporal patterns without assuming a set of pre-existent guiding laws. It is argued that the stability can be the result of a process of convergence to simpler and stable regularities from a more complex lower level. According to this project, if successful, there would be no need to postulate a (mysterious) intermediate category between logical necessity and pure contingency. Similarly, there would be no need to postulate a (mysterious) set of pre-existent governing laws. Part I of the thesis motivates part II, mostly by arguing why further explanation of the notions of physical necessity and governing laws should be welcomed (chapter 1), and by studying the plausibility of a lawless fundamental level (chapters 2 and 3). Given so, part II develops the explanation of formation of simpler and stable behavior from a more complex underlying level. (shrink)

: Models that fail to satisfy the Markov condition are unstable in the sense that changes in state variable values may cause changes in the values of background variables, and these changes in background lead to predictive error. This sort of error arises exactly from the failure of non-Markovian models to track the set of causal relations upon which the values of response variables depend. The result has implications for discussions of the level of selection: under certain plausible conditions the (...) models of selection presented in such debates will not satisfy the Markov condition when fit to data from real populations. Since this is true both for group and individual level models, models of neither sort correctly represent the causal structure generating, nor correctly explain, the phenomena of interest. (shrink)

Moral choice, as a precursor to behaviour, has an important influence on the success or failure of business entities. According to Rest, 1983, Morality, Moral Behavior and Moral Development (John Wiley & Sons, New York), moral choice is prompted, amongst other things, by a motivational component. With this in mind, data obtained from a sample of four hundred financial sector operatives, employed in a rapidly developing region of China, was used to construct a relatively stable set of motivational typologies (...) which could be used to predict choice within an agency-based context. A non-egoist version of the agency theory was developed, which permitted the modelling of alternative heuristic patterns. Altruists and persons identified as bordering on the verge of being classified as psychological egoists, refused to reorganize their motives when responding to a problem that included both moral hazard and adverse selection criteria. It was also possible to identify certain personal and contextual issues which discriminated between the typologies. (shrink)

A union ultrafilter is an ultrafilter over the finite subsets of ω that has a base of sets of the form ${\text{FU}}\left$, where X is an infinite pairwise disjoint family and ${\text{FU}} = \left\{ {\bigcup {F|F} \in [X]^{ < \omega } \setminus \{ \emptyset \} } \right\}$. The existence of these ultrafilters is not provable from the $ZFC$ axioms, but is known to follow from the assumption that ${\text{cov}}\left = \mathfrak{c}$. In this article we obtain various models of $ZFC$ (...) that satisfy the existence of union ultrafilters while at the same time ${\text{cov}}\left = \mathfrak{c}$. (shrink)

Here, we analyze how the set of nucleotides in the cell is equilibrated and how this generates simple rules that help the cell to organize itself via maintenance of a stable non‐equilibrium state. A major mechanism operating to achieve this state is thermodynamic buffering via high activities of equilibrating enzymes such as adenylate kinase. Under stable non‐equilibrium, the ratios of free and Mg‐bound adenylates, Mg2+ and membrane potentials are interdependent and can be computed. The adenylate status is balanced (...) with the levels of reduced and oxidized pyridine nucleotides through regulated uncoupling of the pyridine nucleotide pool from ATP production in mitochondria, and through oxidation of substrates non‐coupled to NAD+ reduction in peroxisomes. The set of adenylates and pyridine nucleotides constitutes a generalized cell energy status and determines rates of major metabolic fluxes. As the result, fluxes of energy and information become organized spatially and temporally, providing conditions for self‐maintenance of metabolism. (shrink)

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied by Baldwin–Eklof–Trlifaj (...) are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický. (shrink)

The projective plane of Baldwin 695) is model complete in a language with additional constant symbols. The infinite rank bicolored field of Poizat 1339) is not model complete. The finite rank bicolored fields of Baldwin and Holland 371; Notre Dame J. Formal Logic , to appear) are model complete. More generally, the finite rank expansions of a strongly minimal set obtained by adding a ‘random’ unary predicate are almost strongly minimal and model complete provided the strongly minimal set is ‘well-behaved’ (...) and admits ‘exactly rank k formulas’. The last notion is a geometric condition on strongly minimal sets formalized in this paper. (shrink)

We prove that in a continuous ℵ₀-stable theory every type-definable group is definable. The two main ingredients in the proof are: 1. Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and 2. Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.

The class of stable posets is defined and investigated. We give a forcing construction of a universe of set theory which satisfies a weak form of Martin's Axiom and $2^{\aleph_0} > \aleph_1$ and yet some propositions which follow from CH hold in this universe.

The paper defines a measure on the set of stable matchings in the marriage problem. This measure is based on the minimization of the envy difference between the sets of men and women, while preserving stability and selects stable matchings with the least conflict of interest between both groups of agents. The solution concept proposed is called Sex-equal Matching (SEM) and the paper also provides an algorithm to compute the set of SEM.

A first-order structure $\mathfrak {A}$ is called monadically stable iff every expansion of $\mathfrak {A}$ by unary predicates is stable. In this paper we give a classification of the class $\mathcal {M}$ of $\omega $ -categorical monadically stable structure in terms of their automorphism groups. We prove in turn that $\mathcal {M}$ is the smallest class of structures which contains the one-element pure set, is closed under isomorphisms, and is closed under taking finite disjoint unions, infinite copies, (...) and finite index first-order reducts. Using our classification we show that every structure in $\mathcal {M}$ is first-order interdefinable with a finitely bounded homogeneous structure. We also prove that every structure in $\mathcal {M}$ has finitely many reducts up to interdefinability, thereby confirming Thomas’ conjecture for the class $\mathcal {M}$. (shrink)

According to Michael Dummett, we may think of the meaning of an expression as given by the principles governing the use we make of it. The principles regulating our linguistic practices can then be grouped into two broad categories (Dummett 1973: 396, 1991: 211). We might state them as follows: I-principles: state the circumstances under which an assertion of a sentence containing the expression in question is warranted. E-principles: state the consequences of asserting a sentence containing the expression. In the (...) case of the logical constants, we may associate a constant's I-principles with the set of its introduction rules and its E-principles with the set of its elimination rules (Dummett 1973: 454).1. (shrink)

We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with Shelah that if an ω-stable theory has either ENI-DOP or is ENI-NDOP and is ENI-deep, then the set of models of T with universe ω is Borel complete.

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding—to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that stable models of a safe (...) sentence can be characterized by a formula of a simple syntactic form. (shrink)

We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...) (second-order number theory with a -comprehension axiom scheme) is insufficient. We briefly consider his claim to have produced a solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a operator can be introduced in other settings. (shrink)

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding—to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that stable models of a safe (...) sentence can be characterized by a formula of a simple syntactic form. (shrink)

We use exact saturation to study the complexity of unstable theories, showing that a variant of this notion called pseudo-elementary class (PC)-exact saturation meaningfully reflects combinatorial dividing lines. We study PC-exact saturation for stable and simple theories. Among other results, we show that PC-exact saturation characterizes the stability cardinals of size at least continuum of a countable stable theory and, additionally, that simple unstable theories have PC-exact saturation at singular cardinals satisfying mild set-theoretic hypotheses. This had previously been (...) open even for the random graph. We characterize supersimplicity of countable theories in terms of having PC-exact saturation at singular cardinals of countable cofinality. We also consider the local analog of PC-exact saturation, showing that local PC-exact saturation for singular cardinals of countable cofinality characterizes supershort theories. (shrink)

This paper addresses psychological factors that might interfere with informed consent on the part of stable patients as potential early-phase clinical trial participants. Thirty-six semistructured interviews with patients who had either diabetes or gout were conducted. We investigated stable patients’ attitudes towards participating in a fictitious first-in-human trial of a novel intervention. We focused on an in-depth analysis of those statements and explanations that indicated the existence of psychological factors impairing decision-making capacity. Three main themes emerged: insufficient comprehension (...) of the inherent logic of clinical trials, the recourse to trust over comprehension, and visceral factors that override deliberative process. Overall, our results indicate a limited psychological capacity on the part of stable patients to meet the requirements of informed consent as set by Declaration of Helsinki. A redesigned informed consent procedure should take account of these psychological realities. (shrink)

How do we determine the well-being of a person when her preferences are not stable across worlds? Suppose, for instance, that you are considering getting married, and that you know that if you get married, you will prefer being unmarried, and that if you stay unmarried, you will prefer being married. The general problem is to find a stable standard of well-being when the standard is set by preferences that are not stable. In this paper, I shall (...) show that the problem is even worse: inconsistency threatens if we accept both that your desires determine what is good for you and that you must prefer what is better for you. After I have introduced a useful toy model and stated the inconsistency argument, I will go on to discuss a couple of unsuccessful theories and see what we can learn from their mistakes. One important lesson is that how you would have felt about a life had you never led it is irrelevant to the question of how good that life is for you. What counts is how you feel about your life when you are actually leading it. Another lesson is that a life can be better for you even if you would not rank it higher, if you were to lead it. (shrink)