A note on model complete models and generic models
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- by Saharon Shelah
- Proc. Amer. Math. Soc. 34 (1972), 509-514
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294114-X
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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
- Jon Barwise and Abraham Robinson, Completing theories by forcing, Ann. Math. Logic 2 (1970), no. 2, 119–142. MR 272613, DOI 10.1016/0003-4843(70)90008-2
- Jon Barwise (ed.), The syntax and semantics of infinitary languages, Lecture Notes in Mathematics, No. 72, Springer-Verlag, Berlin-New York, 1968. MR 0234827
- 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
- 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 313019
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 509-514
- MSC: Primary 02H10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294114-X
- MathSciNet review: 0294114