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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Complete coinductive theories. I


Author: A. H. Lachlan
Journal: Trans. Amer. Math. Soc. 319 (1990), 209-241
MSC: Primary 03C52; Secondary 03C45, 03C50, 03C65
MathSciNet review: 957082
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Abstract: Let $ T$ be a complete theory over a relational language which has an axiomatization by $ \exists \forall $-sentences. The properties of models of $ T$ are studied. It is shown that quantifier-free formulas are stable. This limited stability is used to show that in $ \exists \forall $-saturated models the elementary types of tuples are determined by their $ \exists$-types and algebraicity is determined by existential formulas. As an application, under the additional assumption that no quantifier-free formula has the FCP, the models $ \mathcal{M}$ of $ T$ are completely characterized in terms of certain 0-definable equivalence relations on cartesian powers of $ M$. This characterization yields a result similar to that of Schmerl for the case in which $ T$ is $ {\aleph _0}$-categorical.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0957082-6
PII: S 0002-9947(1990)0957082-6
Article copyright: © Copyright 1990 American Mathematical Society