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255The iterative conception of setReview of Symbolic Logic 1 (1): 97-110. 2008.The phrase ‘The iterative conception of sets’ conjures up a picture of a particular settheoretic universe – the cumulative hierarchy – and the constant conjunction of phrasewith-picture is so reliable that people tend to think that the cumulative hierarchy is all there is to the iterative conception of sets: if you conceive sets iteratively, then the result is the cumulative hierarchy. In this paper, I shall be arguing that this is a mistake: the iterative conception of set is a good one, for al…Read more
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70Implementing Mathematical Objects in Set TheoryLogique Et Analyse 50 (197): 79-86. 2007.In general little thought is given to the general question of how to implement mathematical objects in set theory. It is clear that—at various times in the past—people have gone to considerable lengths to devise implementations with nice properties. There is a litera- ture on the evolution of the Wiener-Kuratowski ordered pair, and a discussion by Quine of the merits of an ordered-pair implemen- tation that makes every set an ordered pair. The implementation of ordinals as Von Neumann ordinals i…Read more
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248ZF + "every set is the same size as a wellfounded set"Journal of Symbolic Logic 68 (1): 1-4. 2003.Let ZFB be ZF + "every set is the same size as a wellfounded set". Then the following are true. Every sentence true in every (Rieger-Bernays) permutation model of a model of ZF is a theorem of ZFB. (i.e.. ZFB is the theory of Rieger-Bernays permutation models of models of ZF) ZF and ZFAFA are both extensions of ZFB conservative for stratified formulæ. The class of models of ZFB is closed under creation of Rieger-Bernays permutation models
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37Sharvy’s Lucy and Benjamin PuzzleStudia Logica 90 (2). 2008.Sharvy’s puzzle concerns a situation in which common knowledge of two parties is obtained by repeated observation each of the other, no fixed point being reached in finite time. Can a fixed point be reached?
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A Note On Paradoxes In EthicsThe Baltic International Yearbook of Cognition, Logic and Communication 1. 2005.
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16A Consistent Higher‐Order Theory Without a (Higher‐Order) ModelMathematical Logic Quarterly 35 (5): 385-386. 1989.
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45A Consistent Higher-Order Theory Without a ModelZeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (5): 385-386. 1989.
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42Decidable Fragments of the Simple Theory of Types with Infinity and $mathrm{NF}$Notre Dame Journal of Formal Logic 58 (3): 433-451. 2017.We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified se…Read more
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Cambridge UniversityRetired faculty
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Cambridge UniversityRetired faculty
Cambridge, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |