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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
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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] M. Benda, Remarks on countable models, Fund. Math. 81 (1974), 107-119. MR 0371634 (51:7852)
  • [2] S. Shelah, Stability, the f. c. p. and superstability, Ann. Math. Logic 3 (1971), 271-362. MR 0317926 (47:6475)
  • [3] A. Pillay, Theories with exactly three models, and theories with algebraic prime models, J. Symbolic Logic (to appear).

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Keywords: Unstable theory, the order property, tight prime model, theory with few links, algebraic model
Article copyright: © Copyright 1980 American Mathematical Society

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