A model theoretic Baire category theorem for simple theories

Details A model theoretic Baire category theorem for simple theories A model theoretic Baire category theorem for simple theories

2009-12-14

arxiv.org/abs/0912.2591v1

Mathematics

Logic

Scientific paper

We define the class of $\tilde\tau_{low}^f$-sets. This is a class of type-definable sets defined in terms of forking by low formulas. We prove a model theoretic Baire category theorem for $\tilde\tau_{low}^f$-sets in a countable simple theory in which the extension property is first-order and show some of its applications. A typical application is the following. Let $T$ be a countable theory with the wnfcp (weak nonfinite cover property) and assume for every non-algebraic $a$ there exists a non-algebraic $a'\acl(a)$ such that $SU(a')<\omega$. Then there exists a weakly-minimal formula with parameters.

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