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 be a complete theory over a relational language which has an axiomatization by -sentences. The properties of models of are studied. It is shown that existential formulas are stable. A theory of forking and independence based on Boolean combinations of existential formulas in -saturated models of is developed for which the independence relation is shown to satisfy a very strong triviality condition. It follows that is tree-decomposable in the sense of Baldwin and Shelah. It is also shown that if the language is finite, then has a prime model.

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

Article copyright:
© Copyright 1991
American Mathematical Society