Brown and Simpson (1993) considered two versions of the Baire Category Theorem, which they called BCT-I and BCT-II . They showed that BCT-I is provable in RCA0, the subsystem of second order arithmetic specifying some basic algebraic properties of the numbers, induction for Σ 1 sets and the recursive comprehension axiom. Additionally, they showed that BCT-II is not provable in RCA0. Brown and S...