Contents
Research Article
Nonstandard characterizations of recursive saturation and resplendency
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- 12 March 2014, pp. 842-863
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We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model
of PA is recursively saturated iff is nonstandard and -logic is consistent. is resplendent iff is nonstandard, -logic is consistent, and every sentence φ which is consistent in -logic is contained in a full satisfaction class for . Thus, for models of PA, recursive saturation can be expressed by a (standard) 
-sentence and resplendency by a 
-sentence.
of PA is recursively saturated iff 
-sentence and resplendency by a 
-sentence.Reviews
Keith J. Devlin. Constructibility. Perspectives in mathematical logic. Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1984, xi + 425 pp.
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- 12 March 2014, pp. 864-867
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Herman Rubin and Jean E. Rubin. Equivalents of the axiom of choice, II. Studies in logic and the foundations of mathematics, vol. 116. North-Holland, Amsterdam, New York, and Oxford, 1985, xxviii + 322 pp.
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- 12 March 2014, pp. 867-869
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- 12 March 2014, pp. 869-870
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Saharon Shelah. Differentially closed fields. Israel journal of mathematics, t. 16 (1973), p. 314–328.
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- 12 March 2014, pp. 870-873
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Michael J. O'Donnell. Equational logic as a programming language. Foundations of computing. The MIT Press, Cambridge, Mass., and London, 1985, xv + 296 pp.
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- 12 March 2014, pp. 873-874
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J. F. A. K. van Benthem. The logic of time. A model-theoretic investigation into the varieties of temporal ontology and temporal discourse. Synthese library, vol. 156. D. Reidel Publishing Company, Dordrecht, Boston, and London, 1983, xvi + 260 pp.
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- 12 March 2014, pp. 874-876
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Generalized quantifiers in natural language, edited by Johan van Benthem and Alice ter Meulen, Groningen-Amsterdam studies in semantics, no. 4, Foris Publications, Dordrecht and Cinnaminson, N.J., 1985, vii + 169 pp.—Therein:
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- 02 September 2019, pp. 876-878
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M. J. Cresswell Structured meanings: the semantics of propositional attitudes. Bradford Books. The MIT Press, Cambridge, Mass., and London, 1985, x + 202 pp.
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- 12 March 2014, pp. 878-882
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Meeting Report
Meeting of the Association for Symbolic Logic, Indianapolis, 1986
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- 12 March 2014, pp. 883-887
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Open days in set theory and arithmetic, Jachranka, Poland, 1986
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- 12 March 2014, pp. 888-894
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Other
Notices
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- 12 March 2014, pp. 895-896
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Front matter
JSL volume 52 issue 3 Cover and Front matter
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- 12 March 2014, pp. f1-f2
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Back matter
JSL volume 52 issue 3 Cover and Back matter
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- 12 March 2014, p. b1
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