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1A Consistent Higher‐Order Theory Without a (Higher‐Order) ModelMathematical Logic Quarterly 35 (5): 385-386. 2006.
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2Permutation Models in the Sense of Rieger‐BernaysMathematical Logic Quarterly 33 (3): 201-210. 2006.
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2Permutations and stratified formulae a preservation theoremMathematical Logic Quarterly 36 (5): 385-388. 2006.
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12Yablo's paradox as a theorem of modal logicLogique Et Analyse 59 265-271. 2016.We (further) demystify Yablo's paradox by showing that it can be thought of as the fact that the formula □ (p → □ ¬p) is unsatisfiable in the modal logic KD4 characterised by frames that are strict partial orders without maximal elements. This modal treatment also unifies the two versions of Yablo's paradox, the original version and its dual. © 2019 Elsevier B.V., All rights reserved.
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36Synonymy Questions Concerning the Quine SystemsJournal of Symbolic Logic 90 (4): 1779-1795. 2025.There are a variety of (“alternative”) axiomatic set theories available to mathematicians. It is worth asking how “alternative” they really are. Might they be no more than rephrasings of the theory (ZFC) that we already have? Here we give an account of the status of the Quine systems in this regard. Some are merely ZF in wolves’ clothing; some are genuine wolves.
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50Internal Automorphisms and Antimorphisms of Models of NfJournal of Symbolic Logic 90 (4): 1796-1800. 2025.It is shown that every model of NF admits a permutation model containing an internal automorphism.
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37Permutation Models in the Sense of Rieger‐BernaysMathematical Logic Quarterly 33 (3): 201-210. 1987.
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53Permutation Models in the Sense of Rieger-BernaysZeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (3): 201-210. 1987.
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143The status of the axiom of choice in set theory with a universal setJournal of Symbolic Logic 50 (3): 701-707. 1985.
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177Term models for weak set theories with a universal setJournal of Symbolic Logic 52 (2): 374-387. 1987.
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135Ramsey’s theorem and König’s LemmaArchive for Mathematical Logic 46 (1): 37-42. 2007.We consider the relation between versions of Ramsey’s Theorem and König’s Infinity Lemma, in the absence of the axiom of choice
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158Non-well-foundedness of well-orderable power setsJournal of Symbolic Logic 68 (3): 879-884. 2003.Tarski [5] showed that for any set X, its set w(X) of well-orderable subsets has cardinality strictly greater than that of X, even in the absence of the axiom of choice. We construct a Fraenkel-Mostowski model in which there is an infinite strictly descending sequence under the relation |w (X)| = |Y|. This contrasts with the corresponding situation for power sets, where use of Hartogs' ℵ-function easily establishes that there can be no infinite descending sequence under the relation |P(X)| = |Y|
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199Further consistency and independence results in NF obtained by the permutation methodJournal of Symbolic Logic 48 (2): 236-238. 1983.
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48Reasoning About Theoretical EntitiesWorld Scientific. 2003.As such this book fills a void in the philosophical literature and presents a challenge to every would-be (anti-)reductionist.
Areas of Interest
| Philosophy of Language |
| Philosophy of Mind |