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

Publisher： Cambridge University Press

E-ISSN： 1943-5886|58|2|557-578

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.58, Iss.2, 1993-06, pp. : 557-578

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Abstract

Working within weak subsystems of second-order arithmetic Z 2 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 Z 2, 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.

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