The Baire category theorem in weak subsystems of second-order arithmetic

Abstract

AbstractWorking within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call and , and , show that suffices to prove B.C.T.II. Some model theory of and its importance in view of Hilbert's program is discussed, as well as applications of our results to functional analysis.