On theories having a finite number of nonisomorphic countable models

Publisher： Cambridge University Press

E-ISSN： 1943-5886|50|3|806-808

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.50, Iss.3, 1985-09, pp. : 806-808

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Abstract

In this paper we shall state some interesting facts concerning non-ω-categorical theories which have only finitely many countable models. Although many examples of such theories are known, almost all of them are essentially the same in the following sense: they are obtained from ω-categorical theories, called base theories below, by adding axioms for infinitely many constant symbols. Moreover all known base theories have the (strict) order property in the sense of [6], and so they are unstable. For example, Ehrenfeucht's well-known example which has three countable models has the theory of dense linear order as its base theory.

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