Extensions of Countable Models of Stable Theories

B. Baizhanov & M. Erimbetov

In our report we consider various properties of elementary extensions of finite generated models of stable theories. We introduce the notions of convergence of formula to type [1], the equivality of Fraisse-Shelah-types [2] and study the relations of these notions with the two-cardinality of formulas and the notion of admissible set, considered in [3].

We obtained some sufficient conditions for constructing of chains of countable models with given properties.

[1] B.S. Baizhanov,”Expansion of a model of a weakly o-minimal theory by a family of unary predicates”, accepted by JSL.

[2] B.S. Baizhanov, ”Pairs of models and property NBAM”, Proceedings of Informatics and Control Problems Institute (M. Aidarkhanov and B. Baizhanov, editors), Gylym, Almaty, 1995, .81-89.(in Russian).

[3] M.M. Erimbetov, ”About one property of countable stable theories”, Siberian Mathematical Journal, vol., XXII, N1, 1981, pp. 81-86.

Addresses B. Baizhanov: Institut of Informatics and Control Problems, Academy of Sciences of Kazakhstan, 125, Pushkin, Almaty,480100, Kazakhstan

E-mail: baijan@ipic.academ.alma-ata.su

M. Erimbetov: Institut of Informatics and Control Problems, Academy of Sciences of Kazakhstan, 125, Pushkin, Almaty, 480100, Kazakhstan

E-mail: LNS@ipic.academ.alma-ata.su