Instability and theories with few models
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- by A. Pillay PDF
- Proc. Amer. Math. Soc. 80 (1980), 461-468 Request permission
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
- Miroslav Benda, Remarks on countable models, Fund. Math. 81 (1973/74), no. 2, 107–119. MR 371634, DOI 10.4064/fm-81-2-107-119
- 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 317926, DOI 10.1016/0003-4843(71)90015-5 A. Pillay, Theories with exactly three models, and theories with algebraic prime models, J. Symbolic Logic (to appear).
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 461-468
- MSC: Primary 03C45; Secondary 03C15
- DOI: https://doi.org/10.1090/S0002-9939-1980-0581006-6
- MathSciNet review: 581006