Complete coinductive theories. II

Lachlan, A. H.

doi:10.1090/S0002-9947-1991-1014253-1

Complete coinductive theories. II
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by A. H. Lachlan

Trans. Amer. Math. Soc. 328 (1991), 527-562

DOI: https://doi.org/10.1090/S0002-9947-1991-1014253-1

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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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Remarks on

stable

categorical theories

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