Complete coinductive theories. II
A. H. Lachlan · Transactions of the American Mathematical Society · 1991
Let T T be a complete theory over a relational language which has an axiomatization by ∃ ∀ \exists \forall -sentences. The properties of models of T 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 T is developed for which the independence relation is shown to satisfy a very strong triviality condition. It follows that T T is tree-decomposable in the sense of Baldwin and Shelah. It is also shown that if the language is finite, then T T has a prime model.