Results for 'Dirichlet's Theorem'

999 found
Order:
  1.  53
    The concept of “character” in Dirichlet’s theorem on primes in an arithmetic progression.Jeremy Avigad & Rebecca Morris - 2014 - Archive for History of Exact Sciences 68 (3):265-326.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  2.  93
    Weyl’s Appropriation of Husserl’s and Poincar“s Thought.Richard Feist - 2002 - Synthese 132 (3):273 - 301.
    This article locates Weyl''s philosophy of mathematics and its relationship to his philosophy of science within the epistemological and ontological framework of Husserl''s phenomenology as expressed in the Logical Investigations and Ideas. This interpretation permits a unified reading of Weyl''s scattered philosophical comments in The Continuum and Space-Time-Matter. But the article also indicates that Weyl employed Poincaré''s predicativist concerns to modify Husserl''s semantics and trim Husserl''s ontology. Using Poincaré''s razor to shave Husserl''s beard leads to limitations on the least upper (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  3.  18
    Weyl’s Appropriation of Husserl’s and Poincar“s Thought.Richard Feist - 2002 - Synthese 132 (3):273-301.
    This article locates Weyl’s philosophy of mathematics and its relationship to his philosophy of science within the epistemological and ontological framework of Husserl’s phenomenology as expressed in the Logical Investigations and Ideas. This interpretation permits a unified reading of Weyl’s scattered philosophical comments in The Continuum and Space-Time-Matter. But the article also indicates that Weyl employed Poincar“s predicativist concerns to modify Husserl’s semantics and trim Husserl’s ontology. Using Poincar“s razor to shave Husserl’s beard leads to limitations on the least upper (...)
    Direct download  
     
    Export citation  
     
    Bookmark   6 citations  
  4.  50
    Character and object.Rebecca Morris & Jeremy Avigad - 2016 - Review of Symbolic Logic 9 (3):480-510.
    In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. Modern presentations of the proof are explicitly higher-order, in that they involve quantifying over and summing over Dirichlet characters, which are certain types of functions. The notion of a character is only implicit in Dirichlet’s original proof, and the subsequent history shows a very gradual transition to the modern mode of presentation. In this essay, we (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  5.  15
    Bell's Theorem: The Price of Locality.Tim Maudlin - 2002-01-01 - In Quantum Non‐Locality and Relativity. Tim Maudlin. pp. 6–26.
    This chapter contains sections titled: Polarization Light Quanta The Entangled State How Do They Do It? Bell's Theorem(s) Aspect's Experiment What Is Weird About the Quantum Connection? Appendix A: The GHZ Scheme.
    Direct download  
     
    Export citation  
     
    Bookmark  
  6. Godel's Theorem in Focus.S. G. Shanker (ed.) - 1987 - Routledge.
    A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.
     
    Export citation  
     
    Bookmark   6 citations  
  7.  5
    Gödel's Theorem in Focus.S. G. Shanker - 1987 - Revue Philosophique de la France Et de l'Etranger 182 (2):253-255.
    Direct download  
     
    Export citation  
     
    Bookmark   11 citations  
  8.  30
    Effective Fine‐convergence of Walsh‐Fourier series.Takakazu Mori, Mariko Yasugi & Yoshiki Tsujii - 2008 - Mathematical Logic Quarterly 54 (5):519-534.
    We define the effective integrability of Fine-computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integrals such as the Bounded Convergence Theorem, the Dominated Convergence Theorem, and the Second Mean Value Theorem. It is also proved that the Walsh-Fourier coefficients of an effectively integrable Fine-computable function form a Euclidian computable sequence of reals which converges effectively to zero. This property of convergence is the effectivization of the Walsh-Riemann-Lebesgue Theorem. The article is closed (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  9.  7
    Energy in Newtonian Gravity.Tobias Eklund & Ingemar Bengtsson - 2022 - Foundations of Physics 53 (1):1–14.
    In Newtonian gravity it is a moot question whether energy should be localized in the field or inside matter. An argument from relativity suggests a compromise in which the contribution from the field in vacuum is positive definite. We show that the same compromise is implied by Noether’s theorem applied to a variational principle for perfect fluids, if we assume Dirichlet boundary conditions on the potential. We then analyse a thought experiment due to Bondi and McCrea that gives a (...)
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  10.  7
    An extension of May's Theorem to three alternatives: axiomatizing Minimax voting.Wesley H. Holliday & Eric Pacuit - manuscript
    May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting (...)
    Direct download  
     
    Export citation  
     
    Bookmark  
  11. Bell’s Theorem: Two Neglected Solutions.Louis Vervoort - 2013 - Foundations of Physics 43 (6):769-791.
    Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  12.  50
    Frege's theorem and foundations for arithmetic.Edward N. Zalta - 2012 - In Ed Zalta (ed.), Stanford Encyclopedia of Philosophy. Stanford Encyclopedia of Philosophy.
    The principal goal of this entry is to present Frege's Theorem (i.e., the proof that the Dedekind-Peano axioms for number theory can be derived in second-order logic supplemented only by Hume's Principle) in the most logically perspicuous manner. We strive to present Frege's Theorem by representing the ideas and claims involved in the proof in clear and well-established modern logical notation. This prepares one to better prepared to understand Frege's own notation and derivations, and read Frege's original work (...)
    Direct download  
     
    Export citation  
     
    Bookmark   11 citations  
  13.  53
    Goedel's theorem, the theory of everything, and the future of science and mathematics.Douglas S. Robertson - 2000 - Complexity 5 (5):22-27.
  14. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
    In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.
    Direct download  
     
    Export citation  
     
    Bookmark   7 citations  
  15. Bell's theorem and the foundations of modern physics.F. Barone, A. O. Barut, E. Beltrametti, S. Bergia, R. A. Bertlmann, H. R. Brown, G. C. Ghirardi, D. M. Greenberger, D. Home & M. Jammer - 1991 - Foundations of Physics 21 (8).
  16.  21
    An Escape From Vardanyan’s Theorem.Ana de Almeida Borges & Joost J. Joosten - 2023 - Journal of Symbolic Logic 88 (4):1613-1638.
    Vardanyan’s Theorems [36, 37] state that $\mathsf {QPL}(\mathsf {PA})$ —the quantified provability logic of Peano Arithmetic—is $\Pi ^0_2$ complete, and in particular that this already holds when the language is restricted to a single unary predicate. Moreover, Visser and de Jonge [38] generalized this result to conclude that it is impossible to computably axiomatize the quantified provability logic of a wide class of theories. However, the proof of this fact cannot be performed in a strictly positive signature. The system $\mathsf (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  17.  47
    von Neumann’s Theorem Revisited.Pablo Acuña - 2021 - Foundations of Physics 51 (3):1-29.
    According to a popular narrative, in 1932 von Neumann introduced a theorem that intended to be a proof of the impossibility of hidden variables in quantum mechanics. However, the narrative goes, Bell later spotted a flaw that allegedly shows its irrelevance. Bell’s widely accepted criticism has been challenged by Bub and Dieks: they claim that the proof shows that viable hidden variables theories cannot be theories in Hilbert space. Bub’s and Dieks’ reassessment has been in turn challenged by Mermin (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  18. Szemerédi’s theorem: An exploration of impurity, explanation, and content.Patrick J. Ryan - 2023 - Review of Symbolic Logic 16 (3):700-739.
    In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  19. Bell's Theorem Begs the Question.Joy Christian - manuscript
    I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  20.  51
    Tarski's theorem and liar-like paradoxes.Ming Hsiung - 2014 - Logic Journal of the IGPL 22 (1):24-38.
    Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  21.  58
    Arrow's theorem, ultrafilters, and reverse mathematics.Benedict Eastaugh - forthcoming - Review of Symbolic Logic.
    This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in RCA0. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in RCA0. This approach yields a proof of Arrow's (...) in RCA0, and thus in PRA, since Arrow's theorem can be formalised as a Π01 sentence. Finally we show that Fishburn's possibility theorem for countable societies is equivalent to ACA0 over RCA0. (shrink)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  22.  79
    Bell’s Theorem and the Issue of Determinism and Indeterminism.Michael Esfeld - 2015 - Foundations of Physics 45 (5):471-482.
    The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR experiment. That assumption is one of the premises of Bell’s theorem. I first argue that only a premise to the effect that what determines the choice of the measurement settings is independent of what determines the past state of the measured system is needed for (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  23.  41
    Ramsey's Theorem for Pairs and Provably Recursive Functions.Alexander Kreuzer & Ulrich Kohlenbach - 2009 - Notre Dame Journal of Formal Logic 50 (4):427-444.
    This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  24.  17
    Ehrenfest’s Theorem revisited.Henryk Stanisław Arodź - 2019 - Philosophical Problems in Science 66:73-94.
    Historically, Ehrenfest’s theorem is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  25.  38
    Ramsey’s theorem and König’s Lemma.T. E. Forster & J. K. Truss - 2007 - Archive for Mathematical Logic 46 (1):37-42.
    We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  26.  89
    Löb's theorem as a limitation on mechanism.Michael Detlefsen - 2002 - Minds and Machines 12 (3):353-381.
    We argue that Löb's Theorem implies a limitation on mechanism. Specifically, we argue, via an application of a generalized version of Löb's Theorem, that any particular device known by an observer to be mechanical cannot be used as an epistemic authority (of a particular type) by that observer: either the belief-set of such an authority is not mechanizable or, if it is, there is no identifiable formal system of which the observer can know (or truly believe) it to (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  27.  71
    Frege's theorem in plural logic.Simon Hewitt - manuscript
    A version of Frege's theorem can be proved in a plural logic with pair abstraction. We talk through this and discuss the philosophical implications of the result.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  28. Making Sense of Bell’s Theorem and Quantum Nonlocality.Stephen Boughn - 2017 - Foundations of Physics 47 (5):640-657.
    Bell’s theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell’s theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system. Einstein was repulsed by such “spooky action at a (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  29. Frege’s Theorem: An Introduction.Richard G. Heck - 1999 - The Harvard Review of Philosophy 7 (1):56-73.
    A brief, non-technical introduction to technical and philosophical aspects of Frege's philosophy of arithmetic. The exposition focuses on Frege's Theorem, which states that the axioms of arithmetic are provable, in second-order logic, from a single non-logical axiom, "Hume's Principle", which itself is: The number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   46 citations  
  30. Fermat’s last theorem proved in Hilbert arithmetic. III. The quantum-information unification of Fermat’s last theorem and Gleason’s theorem.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 14 (12):1-30.
    The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  31. Bell’s Theorem without Inequalities and without Unspeakable Information.Adán Cabello - 2005 - Foundations of Physics 35 (11):1927-1934.
    A proof of Bell’s theorem without inequalities is presented in which distant local setups do not need to be aligned, since the required perfect correlations are achieved for any local rotation of the local setups.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  32. Haag’s Theorem, Apparent Inconsistency, and the Empirical Adequacy of Quantum Field Theory.Michael E. Miller - 2015 - British Journal for the Philosophy of Science:axw029.
    Haag's theorem has been interpreted as establishing that quantum field theory cannot consistently represent interacting fields. Earman and Fraser have clarified how it is possible to give mathematically consistent calculations in scattering theory despite the theorem. However, their analysis does not fully address the worry raised by the result. In particular, I argue that their approach fails to be a complete explanation of why Haag's theorem does not undermine claims about the empirical adequacy of particular quantum field (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  33. Putnam’s Theorem on the Complexity of Models.Warren Goldfarb - 2018 - In John Burgess (ed.), Hilary Putnam on Logic and Mathematics. Cham: Springer Verlag.
    No categories
     
    Export citation  
     
    Bookmark  
  34.  22
    Bayes's Theorem.Richard Swinburne (ed.) - 2002 - Oxford and New York: Oxford University Press UK.
    Bayes's theorem is a tool for assessing how probable evidence makes some hypothesis. The papers in this volume consider the worth and applicability of the theorem. Richard Swinburne sets out the philosophical issues. Elliott Sober argues that there are other criteria for assessing hypotheses. Colin Howson, Philip Dawid and John Earman consider how the theorem can be used in statistical science, in weighing evidence in criminal trials, and in assessing evidence for the occurrence of miracles. David Miller (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  35. Bell's theorem in an indeterministic universe.Donald Bedford & Henry P. Stapp - 1995 - Synthese 102 (1):139 - 164.
    A variation of Bell's theorem that deals with the indeterministic case is formulated and proved within the logical framework of Lewis's theory of counterfactuals. The no-faster-than-light-influence condition is expressed in terms of Lewis would counterfactual conditionals. Objections to this procedure raised by certain philosophers of science are examined and answered. The theorem shows that the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence cannot be ascribed to any auxiliary or tacit assumption of (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  36. Arrow's theorem in judgment aggregation.Franz Dietrich & Christian List - 2007 - Social Choice and Welfare 29 (1):19-33.
    In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we (...)
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark   83 citations  
  37.  59
    Ramsey's Theorem and Cone Avoidance.Damir D. Dzhafarov & Carl G. Jockusch - 2009 - Journal of Symbolic Logic 74 (2):557-578.
    It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low₂ homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition $C\,\not \leqslant _T \,H$, where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun's cone avoidance theorem for Ramsey's theorem. We then extend the result to show that every computable (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  38.  8
    Haag’s Theorem, Apparent Inconsistency, and the Empirical Adequacy of Quantum Field Theory.Michael E. Miller - 2018 - British Journal for the Philosophy of Science 69 (3):801-820.
    Haag’s theorem has been interpreted as establishing that quantum field theory cannot consistently represent interacting fields. Earman and Fraser have clarified how it is possible to give mathematically consistent calculations in scattering theory despite the theorem. However, their analysis does not fully address the worry raised by the result. In particular, I argue that their approach fails to be a complete explanation of why Haag’s theorem does not undermine claims about the empirical adequacy of particular quantum field (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  39.  22
    Hindman's theorem: An ultrafilter argument in second order arithmetic.Henry Towsner - 2011 - Journal of Symbolic Logic 76 (1):353 - 360.
    Hindman's Theorem is a prototypical example of a combinatorial theorem with a proof that uses the topology of the ultrafilters. We show how the methods of this proof, including topological arguments about ultrafilters, can be translated into second order arithmetic.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  40.  94
    Lanford’s Theorem and the Emergence of Irreversibility.Jos Uffink & Giovanni Valente - 2015 - Foundations of Physics 45 (4):404-438.
    It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford’s (...) succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all. (shrink)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  41.  40
    Hechler’s theorem for the null ideal.Maxim R. Burke & Masaru Kada - 2004 - Archive for Mathematical Logic 43 (5):703-722.
    We prove the following theorem: For a partially ordered set Q such that every countable subset of Q has a strict upper bound, there is a forcing notion satisfying the countable chain condition such that, in the forcing extension, there is a basis of the null ideal of the real line which is order-isomorphic to Q with respect to set-inclusion. This is a variation of Hechler’s classical result in the theory of forcing. The corresponding theorem for the meager (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  42.  90
    Frege's theorem.Richard G. Heck - 2011 - New York: Clarendon Press.
    The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   35 citations  
  43.  25
    Pincherle's theorem in reverse mathematics and computability theory.Dag Normann & Sam Sanders - 2020 - Annals of Pure and Applied Logic 171 (5):102788.
    We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  44. Craig’s Theorem and the Empirical Underdetermination Thesis Reassessed.Christian List - 1999 - Disputatio 7 (1):28-39.
    This paper reassesses the question of whether Craig’s theorem poses a challenge to Quine's empirical underdetermination thesis. It will be demonstrated that Quine’s account of this issue in his paper “Empirically Equivalent Systems of the World” (1975) is flawed and that Quine makes too strong a concession to the Craigian challenge. It will further be pointed out that Craig’s theorem would threaten the empirical underdetermination thesis only if the set of all relevant observation conditionals could be shown to (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  45.  58
    Vaught's theorem on axiomatizability by a scheme.Albert Visser - 2012 - Bulletin of Symbolic Logic 18 (3):382-402.
    In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  46.  16
    Halin’s infinite ray theorems: Complexity and reverse mathematics.James S. Barnes, Jun Le Goh & Richard A. Shore - forthcoming - Journal of Mathematical Logic.
    Halin in 1965 proved that if a graph has [Formula: see text] many pairwise disjoint rays for each [Formula: see text] then it has infinitely many pairwise disjoint rays. We analyze the complexity of this and other similar results in terms of computable and proof theoretic complexity. The statement of Halin’s theorem and the construction proving it seem very much like standard versions of compactness arguments such as König’s Lemma. Those results, while not computable, are relatively simple. They only (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  47.  34
    Arrow's Theorem with a fixed feasible alternative.John A. Weymark, Aanund Hylland & Allan F. Gibbard - unknown
    Arrow's Theorem, in its social choice function formulation, assumes that all nonempty finite subsets of the universal set of alternatives is potentially a feasible set. We demonstrate that the axioms in Arrow's Theorem, with weak Pareto strengthened to strong Pareto, are consistent if it is assumed that there is a prespecified alternative which is in every feasible set. We further show that if the collection of feasible sets consists of all subsets of alternatives containing a prespecified list of (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  48.  58
    Bell’s Theorem, Realism, and Locality.Peter Lewis - 2019 - In Alberto Cordero (ed.), Philosophers Look at Quantum Mechanics. Springer Verlag.
    According to a recent paper by Tim Maudlin, Bell’s theorem has nothing to tell us about realism or the descriptive completeness of quantum mechanics. What it shows is that quantum mechanics is non-local, no more and no less. What I intend to do in this paper is to challenge Maudlin’s assertion about the import of Bell’s proof. There is much that I agree with in the paper; in particular, it does us the valuable service of demonstrating that Einstein’s objections (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  49. Arrow's Theorem.Michael Morreau - 2014 - Stanford Encyclopedia of Philosophy: N/A.
    Kenneth Arrow’s “impossibility” theorem—or “general possibility” theorem, as he called it—answers a very basic question in the theory of collective decision-making. Say there are some alternatives to choose among. They could be policies, public projects, candidates in an election, distributions of income and labour requirements among the members of a society, or just about anything else. There are some people whose preferences will inform this choice, and the question is: which procedures are there for deriving, from what is (...)
    Direct download  
     
    Export citation  
     
    Bookmark   8 citations  
  50.  32
    Stable Ramsey's Theorem and Measure.Damir D. Dzhafarov - 2011 - Notre Dame Journal of Formal Logic 52 (1):95-112.
    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 (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
1 — 50 / 999