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55The 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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43Further consistency and independence results in NF obtained by the permutation methodJournal of Symbolic Logic 48 (2): 236-238. 1983.
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37Ramsey’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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31Non-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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24Term models for weak set theories with a universal setJournal of Symbolic Logic 52 (2): 374-387. 1987.
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20Reasoning 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.
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15Ramsey’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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4Non-well-foundedness of well-orderable power setsJournal of Symbolic Logic 68 (3): 879-884. 2003.Tarski [5] showed that for any setX, its setω(X) of well-orderable subsets has cardinality strictly greater than that ofX, 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 ∣ω(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.
Areas of Interest
Philosophy of Language |
Philosophy of Mind |