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
$SU(a')<\omega$.