Search results for 'Goedel Theorem' (try it on Scholar)

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  1. I. Aimonetto (1993). Goedel Theorem of Incompleteness. Filosofia 44 (1):113-136.score: 150.0
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  2. I. Aimonetto (1988). The Foundations of the Goedel Theorem-From Peano to Frege and Russell. Filosofia 39 (3):231-249.score: 150.0
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  3. Robert A. Schultz (1980). What Could Self-Reflexiveness Be? Or Goedel's Theorem Goes to Hollywood and Discovers That It's All Done with Mirrors. Semiotica 30 (1-2).score: 120.0
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  4. Geoffrey Hellman (1981). How to Goedel a Frege-Russell: Goedel's Incompleteness Theorem. Noûs 15:451-68.score: 120.0
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  5. Douglas S. Robertson (2000). Goedel's Theorem, the Theory of Everything, and the Future of Science and Mathematics. Complexity 5 (5):22-27.score: 120.0
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  6. U. Fidelman (1999). Goedel's Theorem and Models of the Brain: Possible Hemispheric Basis for Kant's Psychological Ideas. Journal of Mind and Behavior 20 (1):43-56.score: 120.0
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  7. F. RivettiBarbo (1996). A Surreptitious Change in the Designation of a Term: The Foundation of Goedel's Theorem of the Non-Demonstrability of Non-Contradictoriness-A New Metalinguistic Exposition and Philosophical Considerations. Rivista di Filosofia Neo-Scolastica 88 (1):95-128.score: 120.0
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  8. Taner Edis (1998). How Godel's Theorem Supports the Possibility of Machine Intelligence. Minds and Machines 8 (2):251-262.score: 84.0
    Gödel's Theorem is often used in arguments against machine intelligence, suggesting humans are not bound by the rules of any formal system. However, Gödelian arguments can be used to support AI, provided we extend our notion of computation to include devices incorporating random number generators. A complete description scheme can be given for integer functions, by which nonalgorithmic functions are shown to be partly random. Not being restricted to algorithms can be accounted for by the availability of an arbitrary (...)
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  9. Aaron Sloman (1992). The Emperor's Real Mind -- Review of Roger Penrose's The Emperor's New Mind: Concerning Computers Minds and the Laws of Physics. Artificial Intelligence 56 (2-3):355-396.score: 72.0
    "The Emperor's New Mind" by Roger Penrose has received a great deal of both praise and criticism. This review discusses philosophical aspects of the book that form an attack on the "strong" AI thesis. Eight different versions of this thesis are distinguished, and sources of ambiguity diagnosed, including different requirements for relationships between program and behaviour. Excessively strong versions attacked by Penrose (and Searle) are not worth defending or attacking, whereas weaker versions remain problematic. Penrose (like Searle) regards the notion (...)
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  10. Albert E. Lyngzeidetson (1990). Massively Parallel Distributed Processing and a Computationalist Foundation for Cognitive Science. British Journal for the Philosophy of Science 41 (March):121-127.score: 60.0
    My purpose in this brief paper is to consider the implications of a radically different computer architecure to some fundamental problems in the foundations of Cognitive Science. More exactly, I wish to consider the ramifications of the 'Gödel-Minds-Machines' controversy of the late 1960s on a dynamically changing computer architecture which, I venture to suggest, is going to revolutionize which 'functions' of the human mind can and cannot be modelled by (non-human) computational automata. I will proceed on the presupposition that the (...)
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  11. Peter Slezak (1984). Minds, Machines and Self-Reference. Dialectica 38 (1):17-34.score: 60.0
  12. I. J. Good (1969). Godel's Theorem is a Red Herring. British Journal for the Philosophy of Science 19 (February):357-8.score: 42.0
  13. Peter Slezak (1982). Godel's Theorem and the Mind. British Journal for the Philosophy of Science 33 (March):41-52.score: 42.0
  14. William H. Hanson (1971). Mechanism and Godel's Theorem. British Journal for the Philosophy of Science 22 (February):9-16.score: 42.0
  15. David Coder (1969). Godel's Theorem and Mechanism. Philosophy 44 (September):234-7.score: 42.0
  16. Graham Priest (1994). Godel's Theorem and the Mind... Again. In M. Michael & John O'Leary-Hawthorne (eds.), Philosophy in Mind: The Place of Philosophy in the Study of Mind. Kluwer. 41-52.score: 42.0
  17. John R. Lucas (1961). Minds, Machines and Godel. Philosophy 36 (April-July):112-127.score: 36.0
    Goedel's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be true. Essentially, we consider the formula which says, in effect, "This formula is unprovable-in-the-system". If this formula were provable-in-the-system, we should have a contradiction: for if it were provablein-the-system, then it would not be unprovable-in-the-system, so that "This formula is unprovable-in-the-system" would be false: equally, if it were provable-in-the-system, (...)
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  18. Manuel Bremer, Frege's Basic Law V and Cantor's Theorem.score: 24.0
    The following essay reconsiders the ontological and logical issues around Frege’s Basic Law (V). If focuses less on Russell’s Paradox, as most treatments of Frege’s Grundgesetze der Arithmetik (GGA)1 do, but rather on the relation between Frege’s Basic Law (V) and Cantor’s Theorem (CT). So for the most part the inconsistency of Naïve Comprehension (in the context of standard Second Order Logic) will not concern us, but rather the ontological issues central to the conflict between (BLV) and (CT). These (...)
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  19. Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.score: 24.0
    The Gödelian symphony -- Foundations and paradoxes -- This sentence is false -- The liar and Gödel -- Language and metalanguage -- The axiomatic method or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers (...)
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  20. Jacob Stegenga (2013). An Impossibility Theorem for Amalgamating Evidence. Synthese 190 (12):2391-2411.score: 24.0
    Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously “Arrow’s Theorem”. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.
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  21. Saul A. Kripke (2013). The Church-Turing ‘Thesis’ as a Special Corollary of Gödel’s Completeness Theorem. In B. J. Copeland, C. Posy & O. Shagrir (eds.), Computability: Turing, Gödel, Church, and Beyond. MIT Press.score: 24.0
    Traditionally, many writers, following Kleene (1952), thought of the Church-Turing thesis as unprovable by its nature but having various strong arguments in its favor, including Turing’s analysis of human computation. More recently, the beauty, power, and obvious fundamental importance of this analysis, what Turing (1936) calls “argument I,” has led some writers to give an almost exclusive emphasis on this argument as the unique justification for the Church-Turing thesis. In this chapter I advocate an alternative justification, essentially presupposed by Turing (...)
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  22. Sjoerd D. Zwart & Maarten Franssen (2007). An Impossibility Theorem for Verisimilitude. Synthese 158 (1):75 - 92.score: 24.0
    In this paper, we show that Arrow’s well-known impossibility theorem is instrumental in bringing the ongoing discussion about verisimilitude to a more general level of abstraction. After some preparatory technical steps, we show that Arrow’s requirements for voting procedures in social choice are also natural desiderata for a general verisimilitude definition that places content and likeness considerations on the same footing. Our main result states that no qualitative unifying procedure of a functional form can simultaneously satisfy the requirements of (...)
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  23. Christian List & Robert E. Goodin (2001). Epistemic Democracy: Generalizing the Condorcet Jury Theorem. Journal of Political Philosophy 9 (3):277–306.score: 24.0
    This paper generalises the classical Condorcet jury theorem from majority voting over two options to plurality voting over multiple options. The paper further discusses the debate between epistemic and procedural democracy and situates its formal results in that debate. The paper finally compares a number of different social choice procedures for many-option choices in terms of their epistemic merits. An appendix explores the implications of some of the present mathematical results for the question of how probable majority cycles (as (...)
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  24. Adán Cabello (2005). Bell's Theorem Without Inequalities and Without Unspeakable Information. Foundations of Physics 35 (11):1927-1934.score: 24.0
    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.
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  25. Michael E. Cuffaro, On the Significance of the Gottesman-Knill Theorem.score: 24.0
    According to the Gottesman-Knill theorem, quantum algorithms utilising operations chosen from a particular restricted set are efficiently simulable classically. Since some of these algorithms involve entangled states, it is commonly concluded that entanglement is not sufficient to enable quantum computers to outperform classical computers. It is argued in this paper, however, that what the Gottesman-Knill theorem shows us is only that if we limit ourselves to the Gottesman-Knill operations, we will not have used the entanglement with which we (...)
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  26. Franz Dietrich & Christian List (2007). Arrow's Theorem in Judgment Aggregation. Social Choice and Welfare 29 (1):19-33.score: 24.0
    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 (...)
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  27. Jason Brennan (forthcoming). Condorcet's Jury Theorem and the Optimum Number of Voters. Politics.score: 24.0
    Many political theorists and philosophers use Condorcet's Jury Theorem to defend democracy. This paper illustrates an uncomfortable implication of Condorcet's Jury Theorem. Realistically, when the conditions of Condorcet’s Jury Theorem hold, even in very high stakes elections, having more than 100,000 citizens vote does no significant good in securing good political outcomes. On the Condorcet model, unless voters enjoy voting, or unless they produce some other value by voting, then the cost to most voters of voting exceeds (...)
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  28. Kaj B. Hansen (1995). An Inverse of Bell's Theorem. Journal for General Philosophy of Science 26 (1):63 - 74.score: 24.0
    A class of probability functions is studied. This class contains the probability functions of half-spin particles and spinning classical objects. A notion of realisability for these functions is defined. In terms of this notion two versions of Bell's theorem and their inverses are stated and proved.
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  29. Federico Laudisa (2008). Non-Local Realistic Theories and the Scope of the Bell Theorem. Foundations of Physics 38 (12):1110-1132.score: 24.0
    According to a widespread view, the Bell theorem establishes the untenability of so-called ‘local realism’. On the basis of this view, recent proposals by Leggett, Zeilinger and others have been developed according to which it can be proved that even some non-local realistic theories have to be ruled out. As a consequence, within this view the Bell theorem allows one to establish that no reasonable form of realism, be it local or non-local, can be made compatible with the (...)
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  30. Joe Henson (2013). Non-Separability Does Not Relieve the Problem of Bell's Theorem. Foundations of Physics 43 (8):1008-1038.score: 24.0
    This paper addresses arguments that “separability” is an assumption of Bell’s theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as “holism”) will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately.In this article, it is shown that: (a) localised events can be consistently defined without implying (...)
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  31. Luca Incurvati (2009). Does Truth Equal Provability in the Maximal Theory? Analysis 69 (2):233-239.score: 24.0
    According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the (...)
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  32. Louis Vervoort (2013). Bell's Theorem: Two Neglected Solutions. Foundations of Physics 43 (6):769-791.score: 24.0
    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 (...)
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  33. Elizabeth Gould & P. K. Aravind (2010). Isomorphism Between the Peres and Penrose Proofs of the BKS Theorem in Three Dimensions. Foundations of Physics 40 (8):1096-1101.score: 24.0
    It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.
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  34. Catherine Wilson (2000). Plenitude and Compossibility in Leibniz. The Leibniz Review 10:1-20.score: 24.0
    Leibniz entertained the idea that, as a set of “striving possibles” competes for existence, the largest and most perfect world comes into being. The paper proposes 8 criteria for a Leibniz-world. It argues that a) there is no algorithm e.g., one involving pairwise compossibility-testing that can produce even possible Leibniz-worlds; b) individual substances presuppose completed worlds; c) the uniqueness of the actual world is a matter of theological preference, not an outcome of the assembly-process; and d) Goedel’s theorem (...)
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  35. Nikolaos Galatos & Hiroakira Ono (2006). Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics Over FL. Studia Logica 83 (1-3):279 - 308.score: 24.0
    Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
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  36. Hajime Ishihara (2006). Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof. Notre Dame Journal of Formal Logic 47 (2):249-252.score: 24.0
    Classically, weak König's lemma and Brouwer's fan theorem for detachable bars are equivalent. We give a direct constructive proof that the former implies the latter.
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  37. Sigmund Wagner-Tsukamoto (2007). Moral Agency, Profits and the Firm: Economic Revisions to the Friedman Theorem. [REVIEW] Journal of Business Ethics 70 (2):209 - 220.score: 24.0
    The paper reconstructs in economic terms Friedman's theorem that the only social responsibility of firms is to increase their profits while staying within legal and ethical rules. A model of three levels of moral conduct is attributed to the firm: (1) self-interested engagement in the market process itself, which reflects according to classical and neoclassical economics an ethical ideal; (2) the obeying of the "rules of the game," largely legal ones; and (3) the creation of ethical capital, which allows (...)
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  38. Heinz-Dieter Ebbinghaus (1996). Mathematical Logic. Springer.score: 24.0
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...)
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  39. Anya Plutynski (2006). What Was Fisher's Fundamental Theorem of Natural Selection and What Was It For? Studies in History and Philosophy of Science Part C 37 (1):59-82.score: 24.0
    Fisher’s ‘fundamental theorem of natural selection’ is notoriously abstract, and, no less notoriously, many take it to be false. In this paper, I explicate the theorem, examine the role that it played in Fisher’s general project for biology, and analyze why it was so very fundamental for Fisher. I defend Ewens (1989) and Lessard (1997) in the view that the theorem is in fact a true theorem if, as Fisher claimed, ‘the terms employed’ are ‘used strictly (...)
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  40. Robert E. Goodin & Christian List (2006). A Conditional Defense of Plurality Rule: Generalizing May's Theorem in a Restricted Informational Environment. American Journal of Political Science 50 (4):940-949.score: 24.0
    May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a (...)
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  41. Mordecai Waegell, P. K. Aravind, Norman D. Megill & Mladen Pavičić (2011). Parity Proofs of the Bell-Kochen-Specker Theorem Based on the 600-Cell. Foundations of Physics 41 (5):883-904.score: 24.0
    The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 (...)
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  42. Peter Øhrstrøm, Jörg Zeller & Ulrik Sandborg-Petersen (2012). Prior's Defence of Hintikka's Theorem. A Discussion of Prior's 'The Logic of Obligation and the Obligations of the Logician'. Synthese 188 (3):449-454.score: 24.0
    In his paper, The logic of obligation and the obligations of the logician, A.N. Prior considers Hintikka's theorem, according to which a statement cannot be both impossible and permissible. This theorem has been seen as problematic for the very idea of a logic of obligation. However, Prior rejects the view that the logic of obligation cannot be formalised. He sees this resistance against such a view as an important part of what could be called the obligation of the (...)
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  43. Alexander Koller, Ralph Debusmann, Malte Gabsdil & Kristina Striegnitz (2004). Put My Galakmid Coin Into the Dispenser and Kick It: Computational Linguistics and Theorem Proving in a Computer Game. [REVIEW] Journal of Logic, Language and Information 13 (2):187-206.score: 24.0
    We combine state-of-the-art techniques from computational linguisticsand theorem proving to build an engine for playing text adventures,computer games with which the player interacts purely through naturallanguage. The system employs a parser for dependency grammar and ageneration system based on TAG, and has components for resolving andgenerating referring expressions. Most of these modules make heavy useof inferences offered by a modern theorem prover for descriptionlogic. Our game engine solves some problems inherent in classical textadventures, and is an interesting test (...)
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  44. Albert Visser (2012). The Second Incompleteness Theorem and Bounded Interpretations. Studia Logica 100 (1-2):399-418.score: 24.0
    In this paper we formulate a version of Second Incompleteness Theorem. The idea is that a sequential sentence has ‘consistency power’ over a theory if it enables us to construct a bounded interpretation of that theory. An interpretation of V in U is bounded if, for some n , all translations of V -sentences are U -provably equivalent to sentences of complexity less than n . We call a sequential sentence with consistency power over T a pro-consistency statement for (...)
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  45. David Buhagiar, Emmanuel Chetcuti & Anatolij Dvurečenskij (2009). On Gleason's Theorem Without Gleason. Foundations of Physics 39 (6):550-558.score: 24.0
    The original proof of Gleason’s Theorem is very complicated and therefore, any result that can be derived also without the use of Gleason’s Theorem is welcome both in mathematics and mathematical physics. In this paper we reprove some known results that had originally been proved by the use of Gleason’s Theorem, e.g. that on the quantum logic ℒ(H) of all closed subspaces of a Hilbert space H, dim H≥3, there is no finitely additive state whose range is (...)
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  46. Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman (2001). On the Strength of Ramsey's Theorem for Pairs. Journal of Symbolic Logic 66 (1):1-55.score: 24.0
    We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n (...)
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  47. Raul Hakli & Sara Negri (2012). Does the Deduction Theorem Fail for Modal Logic? Synthese 187 (3):849-867.score: 24.0
    Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a (...)
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  48. Damir D. Dzhafarov (2010). Stable Ramsey's Theorem and Measure. Notre Dame Journal of Formal Logic 52 (1):95-112.score: 24.0
    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 (...)
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  49. Karin U. Katz, Mikhail G. Katz & Taras Kudryk (2014). Toward a Clarity of the Extreme Value Theorem. Logica Universalis 8 (2):193-214.score: 24.0
    We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches.
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  50. Johan van Benthem (2007). A New Modal Lindström Theorem. Logica Universalis 1 (1):125-138.score: 24.0
    . We prove new Lindström theorems for the basic modal propositional language, and for some related fragments of first-order logic. We find difficulties with such results for modal languages without a finite-depth property, high-lighting the difference between abstract model theory for fragments and for extensions of first-order logic. In addition we discuss new connections with interpolation properties, and the modal invariance theorem.
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