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)

 

 

Instability and theories with few models


Author: A. Pillay
Journal: Proc. Amer. Math. Soc. 80 (1980), 461-468
MSC: Primary 03C45; Secondary 03C15
MathSciNet review: 581006
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Some results are obtained concerning $ n(T)$, the number of countable models up to isomorphism, of a countable complete first order theory T. It is first proved that if $ n(T) = 3$ and T has a tight prime model, then T is unstable. Secondly, it is proved that if $ n(T)$ is finite and more than one, and T has few links, then T is unstable. Lastly we show that if T has an algebraic model and has few links, then $ n(T)$ is infinite.


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

  • [1] Miroslav Benda, Remarks on countable models, Fund. Math. 81 (1973/74), no. 2, 107–119. Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday, II. MR 0371634
  • [2] Saharon Shelah, Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory, Ann. Math. Logic 3 (1971), no. 3, 271–362. MR 0317926
  • [3] A. Pillay, Theories with exactly three models, and theories with algebraic prime models, J. Symbolic Logic (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03C45, 03C15

Retrieve articles in all journals with MSC: 03C45, 03C15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0581006-6
Keywords: Unstable theory, the order property, tight prime model, theory with few links, algebraic model
Article copyright: © Copyright 1980 American Mathematical Society