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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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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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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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48Book Review. Abstract Objects. Bob Hale. (review)International Studies in Philosophy 24 (3): 146-48. 1992.
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332Some theorems on the expressive limitations of modal languagesJournal of Philosophical Logic 13 (1). 1984.
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485More 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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312Uniform Upper Bounds on Ideals of Turing DegreesJournal of Symbolic Logic 43 (3): 601-612. 1978.
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117An 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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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)
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25Jumping to a Uniform Upper BoundProceedings of the American Mathematical Society 85 (4): 600-602. 1982.A uniform upper bound on a class of Turing degrees is the Turing degree of a function which parametrizes the collection of all functions whose degree is in the given class. I prove that if a is a uniform upper bound on an ideal of degrees then a is the jump of a degree c with this additional property: there is a uniform bound b<a so that b V c < a.
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31Book Review. The Lambda-Calculus. H. P. Barendregt( (review)Philosophical Review 97 (1): 132-7. 1988.
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267Ontological Commitments, Thick and ThinIn George Boolos (ed.), Method, Reason and Language: Essays in Honor of Hilary Putnam, Cambridge University Press. pp. 235-260. 1990.Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example,…Read more
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8An Exact Pair for the Arithmetic Degrees whose join is not a Weak Uniform Upper Bound, in the Recursive Function Theory-Newsletters, No. 28, August-September 1982.
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Book Review. Language and Philosophical Problems. Soren Stenland. (review)History and Philosophy of Logic 253-6. 1993.