Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on model complete models and generic models


Author: Saharon Shelah
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] J. Barwise and A. Robinson, Completing theories by forcing, Ann. Math. Logic 2 (1970), 119-142. MR 0272613 (42:7494)
  • [2] C. C. Chang, Some remarks on model theory of infinitary languages, The Syntax and Semantics of Infinitary Languages, Lecture Notes in Math., no. 72, Springer-Verlag, Berlin and New York, 1968, pp. 36-64. MR 0234827 (38:3141)
  • [3] M. O. Rabin, Diophantine equations and non-standard models of arithmetic, Proc. Internat. Congress Logic, Methodology and Philosophy of Science (1960), Stanford Univ. Press, Stanford, Calif., 1962, pp. 151-158. MR 27 #3540. MR 0153577 (27:3540)
  • [4] J. I. Malitz and W. N. Reinhardt, Maximal models in the language with quantifier ``there exist uncountably many", Pacific J. Math. (to appear). MR 0313019 (47:1574)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02H10

Retrieve articles in all journals with MSC: 02H10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0294114-X
Keywords: Generic models, model complete, omitting types, maximal models
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society