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280The Modal Theory Of Pure Identity And Some Related Decision ProblemsMathematical Logic Quarterly 30 (26-29): 415-423. 1984.Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke co…Read more
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300Individual-actualism and three-valued modal logics, part 1: Model-theoretic semanticsJournal of Philosophical Logic 15 (4). 1986.
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22Book Review. Principles of Intuitionism. Michael Dummett (review)Philosophical Review 91 (2): 253-62. 1982.
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14A Minimal Upper Bound on a Sequence of Turing Degrees Which Represents that SequencePacific Journal of Mathematics 108 (1): 115-119. 1983.
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229Where Do the Cardinal Numbers Come From?Synthese 84 (3): 347-407. 1990.This paper presents a model-theoretic semantics for discourse "about" natural numbers, one that captures what I call "the mathematical-object picture", but avoids what I can "the mathematical-object theory".
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61Review: Jaakko Hintikka, The Principles of Mathematics Revisited (review)Journal of Symbolic Logic 63 (4): 1615-1623. 1998.
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742Logicism and the ontological commitments of arithmeticJournal of Philosophy 81 (3): 123-149. 1984.
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51Book Review. Logic and Arithmetic, Volume I. D Bostock. (review)Journal of Philosophy 73 (6): 149-57. 1976.
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36Annual meeting of the Association for Symbolic Logic, New York City, December 1987Journal of Symbolic Logic 53 (4): 1287-1299. 1988.
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266Upper bounds on locally countable admissible initial segments of a Turing degree hierarchyJournal of Symbolic Logic 46 (4): 753-760. 1981.Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on results of Jensen and is detailed …Read more
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251Individual-actualism and three-valued modal logics, part 2: Natural-deduction formalizationsJournal of Philosophical Logic 16 (1). 1987.
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19Book Review. Reflections. Kurt Godel. (review)THe Journal for Symbolic Logic 54 (3): 1095-98. 1989.
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48Book Review. Abstract Objects. Bob Hale. (review)International Studies in Philosophy 24 (3): 146-48. 1992.
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21Wang Hao. Reflections on Kurt Gödel. Bradford books. The MIT Press, Cambridge, Mass., and London, 1987, xxvi + 336 pp (review)Journal of Symbolic Logic 54 (3): 1095-1098. 1989.
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332Some theorems on the expressive limitations of modal languagesJournal of Philosophical Logic 13 (1). 1984.
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486More about uniform upper Bounds on ideals of Turing degreesJournal of Symbolic Logic 48 (2): 441-457. 1983.Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on I never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible …Read more
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229Finite level borel games and a problem concerning the jump hierarchyJournal of Symbolic Logic 49 (4): 1301-1318. 1984.
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Book Review. Logic and Its Limits. P Shaw. (review)History and Philosophy of Logic 5 (2): 251. 1984.
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118An Exact Pair for the Arithmetic Degrees Whose Join is Not a Weak Uniform Upper BoundRecursive Function Theory-Newsletters 28. 1982.Proof uses forcing on perfect trees for 2-quantifier sentences in the language of arithmetic. The result extends to exact pairs for the hyperarithmetic degrees.
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312Uniform Upper Bounds on Ideals of Turing DegreesJournal of Symbolic Logic 43 (3): 601-612. 1978.
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96On some concepts associated with finite cardinal numbersBehavioral and Brain Sciences 31 (6): 657-658. 2008.I catalog several concepts associated with finite cardinals, and then invoke them to interpret and evaluate several passages in Rips et al.'s target article. Like the literature it discusses, the article seems overly quick to ascribe the possession of certain concepts to children (and of set-theoretic concepts to non-mathematicians)