
13Decidable Fragments of the Simple Theory of Types with Infinity and $mathrm{NF}$Notre Dame Journal of Formal Logic 58 (3): 433451. 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 quantifierfree, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifierfree. This shows that NF decides every stratified se…Read more

Zf + “every Set Is The Same Size As A Wellfounded Set”Journal of Symbolic Logic 68 (1): 14. 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 permutation model of a model of ZF is a theorem of ZFB. ZF and ZFAFA are both extensions of ZFB conservative for stratified formul{\ae}.{The class of models of ZFB is closed under creation of RiegerBernays permutation models.

7Sharvy’s Lucy and Benjamin PuzzleStudia Logica 90 (2): 249256. 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?

19A Consistent HigherOrder Theory Without a ModelZeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (5): 385386. 1989.

A Note On Paradoxes In EthicsThe Baltic International Yearbook of Cognition, Logic and Communication 1. 2005.

4A Consistent Higher‐Order Theory Without a (Higher‐Order) ModelMathematical Logic Quarterly 35 (5): 385386. 1989.

41Implementing Mathematical Objects in Set TheoryLogique Et Analyse 50 (197): 7986. 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 WienerKuratowski ordered pair, and a discussion by Quine of the merits of an orderedpair implemen tation that makes every set an ordered pair. The implementation of ordinals as Von Neumann ordinals i…Read more

83Yablo's Paradox and the Omitting Types Theorem for Propositional LanguagesLogique Et Analyse 54 (215): 323. 2011.

54An OrderTheoretic Account of Some SetTheoretic ParadoxesNotre Dame Journal of Formal Logic 52 (1): 119. 2011.We present an ordertheoretic analysis of settheoretic paradoxes. This analysis will show that a large variety of purely settheoretic paradoxes (including the various Russell paradoxes as well as all the familiar implementations of the paradoxes of Mirimanoff and BuraliForti) are all instances of a single limitative phenomenon

16Permutations and Wellfoundedness: The True Meaning of the Bizarre Arithmetic of Quine's NFJournal of Symbolic Logic 71 (1). 2006.It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the Tfunction which is peculiar to NF turn out to be equivalent to the truthincertainpermutationmodels of assertions which have perfectly sensible ZFstyle meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente

23Sharvy’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?

188The iterative conception of setReview of Symbolic Logic 1 (1): 97110. 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 phrasewithpicture 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

25Finitetoone mapsJournal of Symbolic Logic 68 (4): 12511253. 2003.It is shown in ZF (without choice) that if there is a finitetoone map P(X) → X, then X is finite

14Alternative Set TheoriesIn Dov Gabbay (ed.), The Handbook of the History of Logic, Elsevier. 2009.
Areas of Interest
Philosophy of Language 
Philosophy of Mind 