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
MathSciNet review: 0294114
Full-text PDF Free Access

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] Jon Barwise and Abraham Robinson, Completing theories by forcing, Ann. Math. Logic 2 (1970), no. 2, 119–142. MR 0272613
  • [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

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