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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Complete coinductive theories. II

Author: A. H. Lachlan
Journal: Trans. Amer. Math. Soc. 328 (1991), 527-562
MSC: Primary 03C45; Secondary 03C68
MathSciNet review: 1014253
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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 existential formulas are stable. A theory of forking and independence based on Boolean combinations of existential formulas in $ \exists \forall $-saturated models of $ T$ is developed for which the independence relation is shown to satisfy a very strong triviality condition. It follows that $ T$ is tree-decomposable in the sense of Baldwin and Shelah. It is also shown that if the language is finite, then $ T$ has a prime model.

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Article copyright: © Copyright 1991 American Mathematical Society