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A note on model complete models and generic models

Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 34 (1972), 509-514
MSC: Primary 02H10
MathSciNet review: 0294114
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Abstract: We prove that there are many maximum model complete (= generic) models, and that there exists an (uncountable) theory with no generic models.

References [Enhancements On Off] (What's this?)

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  • [2] The syntax and semantics of infinitary languages, Edited by Jon Barwise. Lecture Notes in Mathematics, No. 72, Springer-Verlag, Berlin-New York, 1968. MR 0234827
  • [3] Michael O. Rabin, Diophantine equations and non-standard models of arithmetic, Logic, Methodology and Philosophy of Science (Proc. 1960 Internat. Congr.), Stanford Univ. Press, Stanford, Calif., 1962, pp. 151–158. MR 0153577
  • [4] J. I. Malitz and W. N. Reinhardt, Maximal models in the language with quantifier “there exist uncountably many”, Pacific J. Math. 40 (1972), 139–155. MR 0313019

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Keywords: Generic models, model complete, omitting types, maximal models
Article copyright: © Copyright 1972 American Mathematical Society