Instability and theories with few models
Abstract: Some results are obtained concerning , the number of countable models up to isomorphism, of a countable complete first order theory T. It is first proved that if and T has a tight prime model, then T is unstable. Secondly, it is proved that if 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 is infinite.
-  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, https://doi.org/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 0317926, https://doi.org/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).
- M. Benda, Remarks on countable models, Fund. Math. 81 (1974), 107-119. MR 0371634 (51:7852)
- S. Shelah, Stability, the f. c. p. and superstability, Ann. Math. Logic 3 (1971), 271-362. MR 0317926 (47:6475)
- A. Pillay, Theories with exactly three models, and theories with algebraic prime models, J. Symbolic Logic (to appear).
Keywords: Unstable theory, the order property, tight prime model, theory with few links, algebraic model
Article copyright: © Copyright 1980 American Mathematical Society