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60Review: Jaakko Hintikka, The Principles of Mathematics Revisited (review)Journal of Symbolic Logic 63 (4): 1615-1623. 1998.
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733Logicism and the ontological commitments of arithmeticJournal of Philosophy 81 (3): 123-149. 1984.
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50Book Review. Logic and Arithmetic, Volume I. D Bostock. (review)Journal of Philosophy 73 (6): 149-57. 1976.
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35Annual meeting of the Association for Symbolic Logic, New York City, December 1987Journal of Symbolic Logic 53 (4): 1287-1299. 1988.
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257Upper 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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249Individual-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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47Book 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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330Some theorems on the expressive limitations of modal languagesJournal of Philosophical Logic 13 (1). 1984.
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482More 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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223Finite 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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113An 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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304Uniform Upper Bounds on Ideals of Turing DegreesJournal of Symbolic Logic 43 (3): 601-612. 1978.
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95On 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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24Jumping 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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30Book Review. The Lambda-Calculus. H. P. Barendregt( (review)Philosophical Review 97 (1): 132-7. 1988.