The Baire algebra of a topological space X is the quotient of the algebra of all subsets of X modulo the meager sets. We show that this Boolean algebra can be endowed with a natural closure operator, resulting in a closure algebra which we denote $\mathbf {Baire}(X)$. We identify the modal logic of such algebras to be the well-known system $\mathsf {S5}$, and prove soundness and strong completeness for the cases where X is crowded and either completely metrizable and continuum-sized (...) or locally compact Hausdorff. We also show that every extension of $\mathsf {S5}$ is the modal logic of a subalgebra of $\mathbf {Baire}(X)$, and that soundness and strong completeness also holds in the language with the universal modality. (shrink)

We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these characterizations to prove new results in computable analysis and effective topology. We also apply the technique of computable compactness to give new and less combinatorially involved proofs of known results from the literature. Some of these results do not have computable compactness or compact spaces in their statements, and thus (...) these applications are not necessarily direct or expected. (shrink)

A model for gauge theories over a compact Lie group is described using R × S3 as background space. The U(1) and SU(2) gauge theories are considered as particular examples, and a comparison with other results is given. Our results differ from those of Carmeli and MalinFound. Phys. 16, 791 (1986);17, 193 (1987)] by a supplementary term in the curvature tensor due to the noncommutativity of derivatives used on R × S3 space. Some observations about supersymmetry and gravity on R (...) × S3 space are also given. (shrink)

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of “non-existing” objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non (...) unlike the notion of “truth at world” found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

The study of continuous group actions is ubiquitous in mathematics, and perhaps the most general kinds of actions for which we can hope to prove theorems in just ZFC are those where a Polish group acts on a Polish space.For this general class we can find works such as [29] that build on ideas from ergodic theory and examine actions of locally compact groups in both the measure theoretic and topological contexts. On the other hand a text in model theory, (...) such as [12], will typically consider issues bearing on the actions by the symmetric group of all permutations of the integers. More generally [1] shows that the orbit equivalence relations induced by closed subgroups of the infinite symmetric group can be reduced to the isomorphism relation on corresponding classes of countable models.This paper considers a third category formed by the continuous actions of separable Banach spaces on Polish spaces. These examples cannot be subsumed under the two earlier headings, and it is known from [10] that theBorel cardinalitiesof the quotient spaces that arise from such actions are incomparable with the equivalence relations induced by the symmetric group or any locally compact Polish group action.One of the first things to be addressed concerns the complexity of these equivalence relations. This question forappears in [1]. (shrink)

Public deliberation about health policy in the United States often hinges on two untenable basic assumptions about political legitimacy. The first assumption, common in public debate throughout the United States, is that federal oversight of health care is justified under a federal compact binding all citizens. This assumption is false because the federal compact precludes such oversight. Indeed, the ascendancy of national government (and demise of federalism) over the past 70 years was engineered through the subversion of the federal compact, (...) creating an expansive legitimation gap. The second assumption—that political legitimacy can be established through appeals to expert consensus about fundamental conceptions of justice or human rights—is prevalent among bioethicists. I argue that this assumption is illicit because it hinges on a weak, rationalistic form of majoritarian democracy that conflates public acquiescence with public approval. If the public mission of academic bioethics involves protecting the integrity of public deliberation, then these two basic assumptions should be challenged. (shrink)

Farmers in developed countries have established various tillage practices for crop production. These include plowing, disking, subsoiling, harrowing, field cultivating, rotary hoeing, and row-crop cultivating. But these conventional tillage practices necessitate the use of heavy equipment that often causes soil compaction, impairs soil physical conditions, and creates conditions leading to soil erosion. Many Western countries, studying their conventional tillage systems through the new perspective of sustainable approaches to agriculture, are developing new tillage practices, called conservation tillage, which limit tillage to (...) essential operations and prevent damage to soil. The majority of the small-scale farmers in developing countries use indigenous tillage systems. These are low-cost, locally adapted technologies that reflect considerable knowledge of sustainable agriculture. Ironically, the new conservation tillage systems currently being developed in the West have many characteristics of indigenous tillage systems. This paper compares conventional, conservation, and indigenous tillage practices, using examples from the United States and India, and concludes that, for sustainable food production, indigenous tillage practices in developing countries should continue to be used. (shrink)

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive (...) on open sets. (shrink)

A metric space is said to be locally non-compact if every neighborhood contains a sequence that is eventually bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non-compact iff it is without isolated points.The result has an interesting consequence in computable analysis: If a complete metric space has a computable witness that it is without isolated points, then every neighborhood contains a computable sequence (...) that is eventually computably bounded away from every computable element of the space. (shrink)

An unorthodox cosmology is based on a notion of “standpoint,” distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age, boost of matter energy-momentum in standpoint rest frame and displacement of matter location in a compact U⊗O/O spacetime attached to standpoint. An “initial” condition is characterized by a huge dimensionless parameter α that breaks dilation invariance. Four major (...) length scales are recognized, called “Planck,” “particle,” “lab,” and “Hubble,” with separations controlled by α; all physical concepts, including spacetime, depend on wideness of scale separation. (shrink)

The tree-based data structure of -tree for propositional formulas is introduced in an improved and optimised form. The -trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal form A (...) at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem. (shrink)

The tree-based data structure of △-tree for propositional formulas is introduced in an improved and optimised form. The △-trees allow a compact representation for negation normal forms as well as for a number of reduction strategies in order to consider only those occurrences of literals which are relevant for the satisfiability of the input formula. These reduction strategies are divided into two subsets (meaning- and satisfiability-preserving transformations) and can be used to decrease the size of a negation normal form A (...) at (at most) quadratic cost. The reduction strategies are aimed at decreasing the number of required branchings and, therefore, these strategies allow to limit the size of the search space for the SAT problem. (shrink)

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non (...) unlike the notion of "truth at world" found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization). (shrink)

Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a contextual (...) DDT iff it is protoalgebraic and gives rise to a dually Brouwerian semilattice of compact deductive filters in every finitely generated algebra of the corresponding type. Any such system is filter distributive, although it may lack the filter extension property. More generally, filter distributivity and modularity are characterized for all finitary systems with a local contextual DDT, and several examples are discussed. For algebraizable logics, the well-known correspondence between the DDT and the equational definability of principal congruences is adapted to the contextual case. (shrink)

Let X be a compact metric space. A closed set K $\subseteq$ X is located if the distance function d(x, K) exists as a continuous real-valued function on X; weakly located if the predicate d(x, K) $>$ r is Σ 0 1 allowing parameters. The purpose of this paper is to explore the concepts of located and weakly located subsets of a compact separable metric space in the context of subsystems of second order arithmetic such as RCA 0 , WKL (...) 0 and ACA 0 . We also give some applications of these concepts by discussing some versions of the Tietze extension theorem. In particular we prove an RCA 0 version of this result for weakly located closed sets. (shrink)

We present a class of normal modal calculi PFD, whose syntax is endowed with operators M r, one for each r [0,1] : if a is sentence, M r is to he read the probability that a is true is strictly greater than r and to he evaluated as true or false in every world of a F-restricted probabilistic kripkean model. Every such a model is a kripkean model, enriched by a family of regular probability evaluations with range in a (...) fixed finite subset F of [0,1] : there is one such a function for every world w, P F, and this allows to evaluate M ra as true in the world w iff p F r.For every fixed F as before, suitable axioms and rules are displayed, so that the resulting system P FD is complete and compact with respect to the class of all the F-restricted probabilistic kripkean models. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.

This paper outlines the academic architecture of CityLab as graduate program course initiative and Principles of Responsible Management Education capstone exemplar. When the United Nations launched the Millennium Goals in 2000 to focus global development on humanity rather than GDP, the Global Compact was launched as a collateral effort, challenging business, government, and social sector leaders to transform the global economic system. In 2007, the Six PRME focused on business schools, challenging them to reorient their curricula towards preparing students to (...) lead the world in building “an inclusive and sustainable economy.” CityLab is an example of innovating the learning experience and challenging learners to take leadership roles in efforts to enhance the value of livable cities as the foundation of an inclusive and sustainable global economy for the Urban Century. (shrink)

In this note we show that the Axiom of Countable Choice is equivalent to two statements from the theory of pseudometric spaces: the first of them is a well-known characterization of uniform continuity for functions between metric spaces, and the second declares that sequentially compact pseudometric spaces are \—meaning that all real valued, continuous functions defined on these spaces are necessarily uniformly continuous.

The aim of Nordenstam’s capable but compact book is to examine the analytic-synthetic distinction and its relationship to empiricism in light of the criticisms expressed by W. V. Quine’s "Two Dogmas of Empiricism," M. G. White’s "The Analytic and the Synthetic: An Untenable Dualism," and N. Goodman’s "On Likeness of Meaning." Nordenstam cites Pasch’s summary of the controversy: "Empiricism presupposes a sharp distinction between analytic and synthetic statements. There is no sharp distinction between analytic and synthetic statements in natural languages (...) but only in artificial languages. But the artificial language approach is incompatible with empiricism. Therefore, empiricism has to be abandoned, or at least it has to be modified." In addressing this argument, Nordenstam begins with an explication of some of the basic concepts: the various interpretations of the principle of analyticity, the gradualist positions of Quine et al., the principle of empiricism, and the relationship between these two principles. From this analysis he concludes that one can legitimately hold the principle of empiricism and still reject the principle of analyticity, thereby denying the first assumption of the above argument. Focusing attention on the opposition to the analytic-synthetic distinction, he introduces a number of criticisms by Quine et al. of some twelve common definitions of "analytic statement" involving the notions of synonymy, state-descriptions, and semantical rules of artificial languages. Here Nordenstam’s suggestion is that the resultant criteria of analyticity and synonymy demanded by Quine et al. are excessively stringent. (shrink)

ABSTRACT Modern elephant tusk is compared with Byzantine plaques as regards the surface microstructure by means of macrophotography. We are thus able to illustrate the differences between elephant bone and elephant tusk, whereas many exhibitions and publications wrongly refer to ivory as elephant bone. It is not uncommon in Greek and German literature to confuse elephant bone with elephant tusk. Bone is porous and white, whereas ivory is yellowish and compact with characteristic dentine structural lines. The structural lines of dentine (...) in plates made of organic mineralized tissues are diagnostic features of ivory that conclusively differentiate it from elephant bone. Dentine is also more compact than bone. Unlike bone, which is inexpensive and common, ivory is expensive and rare in keeping with the stature, wealth and power of Byzantine Emperors. (shrink)

Costa de Beauregard here offers a compact exposition of his views concerning the statistical nature of temporal phenomena, views complementary to those included in the companion volume, La Notion de Temps. The "science of time," according to Costa de Beauregard, can be subsumed under two important principles: the first trading on the Aristotelian equivalence between time and motion, the second based on those "irreversible" phenomena which define an "arrow of time." This book deals expressly with this second principle, touching interestingly (...) on the related problems of cybernetics, entropy and information theory.—G. S. M. (shrink)

Although debates over carbon taxes and trading schemes, over carbon offsets and compact fluorescents are important, our efforts to address the environmental challenges that we face will fall short unless and until we also set about the difficult work of reconceiving who we are and how we are related to our processive cosmos. What is needed, I argue, are new ways of thinking and acting grounded in new ways of understanding ourselves and our relationship to the world, ways of understanding (...) that recognize our fundamental interdependence and interconnection with everyone and everything in the cosmos, ways of understanding that recognize the intrinsic beauty and value of every form of existence. What is needed, I suggest, is a moral philosophy grounded in Alfred North Whitehead's philosophy of organism. It is the primary aim of this essay to defend the value of a moral philosophy inspired by Whitehead's organic, beauty-centered conception of reality. (shrink)

Aristotle was the first philosopher in the Western tradition to address politics systematically and empirically, and he remains a central figure in political theory. This essential volume presents Aristotle's complete political writings—including his Politics, Economics, and Constitution of Athens—in their most authoritative translations, taken from the complete works that is universally recognized as the standard English edition. Edited by Jonathan Barnes, one of the world’s leading scholars of ancient philosophy, and with an illuminating introduction by Melissa Lane, an authority on (...) ancient political philosophy, this compact but comprehensive volume will be invaluable for all students of politics, philosophy, classics, or Western thought. (shrink)

Business cycle theory is a broad and disparate field. Different schools of thought offer alternative explanations for cycles, often using different mathematical methods. This book provides academics and graduate students of economics with a compact and accessible exposition of business cycle theory since Keynes. The author places the main theories -- Keynesian economics, monetarism, new classical economics, the real business cycles theory, and new Keynesian economics -- in an historical context by presenting them in the chronological order of their appearance (...) and highlighting their differences and commonalities. He minimizes the necessary mathematical prerequisites by using a unifying mathematical approach: stochastic second-order difference equations, which is explained in detail. Throughout the book, the international dimension of business cycles is acknowledged. The theoretical results obtained are set alongside empirical facts in separate boxes. Each chapter finishes with a set of problems designed to deepen the reader's understanding of the theories presented, and further reading sections which provide access to related material. (shrink)

A connection viewed from the perspective of integration has the Bianchi identities as constraints. It is shown that the removal of these constraints admits a natural solution on manifolds endowed with a metric and teleparallelism. In the process, the equations of structure and the Bianchi identities take standard forms of field equations and conservation laws.The Levi-Civita (part of the) connection ends up as the potential for the gravity sector, where the source is geometric and tensorial and contains an explicit gravitational (...) contribution.Nonlinear field equations for the torsion result. In a “low-energy” approximation (linearity andlow energy-momentumtransfer), the postulate that only charge and velocities contribute to the source transforms these equations into the Maxwell system. Moreover, the affine geodesics become the equations of motion of special relativity with Lorentz force in the same approximation [J. G. Vargas,Found. Phys. 21, 379 (1991)]. The field equations for the torsion must then be viewed as applying to an electromagnetic/strong interaction.A classical unified theory thus arises where the underlying geometry confers their contrasting characters to Maxwell-Lorentz electrodynamics and to an Einstein's-like theory of gravity. The highly compact field equations must, however, be developed in phase-spacetime, since the connection is velocity-dependent, i.e., Finsler-like.Further opportunities for similarities with present-day physics are discussed: (a) teleparallelism allows for the formulation of the torsion sector of the theory as a flat space theory with concomitant point-dependent transformations; (b) spinors should replace Lorentz frames in their role as the subjects to which the connection refers; (c) the Dirac equation consistent with the frame bundle for a velocity-dependent metric with Lorentz signature generates a weak-like interaction in the torsion sector. (shrink)

We continue the work of [14, 3, 1, 19, 16, 4, 12, 11, 20] investigating the strength of set existence axioms needed for separable Banach space theory. We show that the separation theorem for open convex sets is equivalent to WKL 0 over RCA 0 . We show that the separation theorem for separably closed convex sets is equivalent to ACA 0 over RCA 0 . Our strategy for proving these geometrical Hahn-Banach theorems is to reduce to the finite-dimensional case (...) by means of a compactness argument. (shrink)

This compact and innovative book tackles one of the central issues in drug policy: the lack of a coherent conceptual structure for thinking about drugs. Drugs generally fall into one of seven categories: prescription, over the counter, alternative medicine, common-use drugs like alcohol, tobacco and caffeine; religious-use, sports enhancement; and of course illegal street drugs like cocaine and marijuana. Our thinking and policies varies wildly from one to the other, with inconsistencies that derive more from cultural and social values than (...) from medical or scientific facts. Penalties exist for steroid use, while herbal remedies or cold medication are legal. Native Americans may legally use peyote, but others may not. Penalties may vary for using different forms of the same drug, such as crack vs. powder cocaine. Herbal remedies are unregulated by the FDA; but medical marijuana is illegal in most states. Battin and her contributors lay a foundation for a wiser drug policy by promoting consistency and coherency in the discussion of drug issues and by encouraging a unique dialogue across disciplines. The contributors are an interdisciplinary group of scholars mostly based at the University of Utah, and include a pharmacologist, a psychiatrist, a toxicologist, a trial court judge, a law professor, an attorney, a diatary specialist, a physician, a health expert on substance abuse, and Battin herself who is a philosopher. They consider questions like the historical development of current policy and the rationales for it; scientific views on how drugs actually cause harm; how to define the key notions of harm and addiction; and ways in which drug policy can be made more consistent. They conclude with an examination of the implications of a consistent policy for various disciplines and society generally. The book is written accessibly with little need for expert knowledge, and will appeal to a diverse audience of philosophers, bioethicists, clinicians, policy makers, law enforcement, legal scholars and practitioners, social workers, and general readers, as well as to students in areas like pharmacy, medicine, law, nursing, sociology, social work, psychology, and bioethics. (shrink)

Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.

This workshop introduced the concept of global business citizenship and explored several ways to use the model, its underlying theory, and cases representing it in classroom teaching. Links to peace studies, organizational change exercises, accountability resources, and the use of United Nations Global Compact case studies all received attention.

Lascar described E KP as a composition of E L and the topological closure of E L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an (...) affine copy of G and in M′ we have the structure of M and the action of G on X. We prove that the Lascar group of M′ is a semi-direct product of the Lascar group of M and G/G L . We discuss the relationship between G-compactness of M and M′. This example may yield new examples of non-G-compact theories. (shrink)

We introduce the notion of hereditary G-compactness. We provide a sufficient condition for a poset to not be hereditarily G-compact, which we use to show that any linear order is not hereditarily G-compact. Assuming that a long-standing conjecture about unstable NIP theories holds, this implies that an NIP theory is hereditarily G-compact if and only if it is stable -categorical theories). We show that if G is definable over A in a hereditarily G-compact theory, then \. We also include (...) a brief survey of sufficient conditions for G-compactness, with particular focus on those which can be used to prove or disprove hereditary G-compactness for some theories. (shrink)

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ${X \subseteq G}$ then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

Given a compact Polish space E and the hyperspace of its compact subsets , we consider Gδσ-ideals of compact subsets of E. Solecki has shown that any σ-ideal in a broad natural class of Gδ ideals can be represented via a compact subset of ; in this article we examine the behaviour of Gδ subsets of E with respect to the representing set. Given an ideal I in this class, we construct a representing set that recognises a compact subset of (...) E as being “small” precisely when it is in I, and recognises a Gδ subset of E as being “small” precisely when it is covered by countably many compact sets from I. (shrink)