Journal of Symbolic Logic

The Baire Category Theorem in Weak Subsystems of Second-Order Arithmetic

Douglas K. Brown and Stephen G. Simpson

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Working within weak subsystems of second-order arithmetic $\mathbf{Z}_2$ we consider two versions of the Baire Category theorem which are not equivalent over the base system $RCA_0$. We show that one version (B.C.T.I) is provable in $RCA_0$ while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of $\mathbf{Z}_2$, which we call $RCA^+_0$ and $WKL^+_0$, and show that $RCA^+_0$ suffices to prove B.C.T.II. Some model theory of $WKL^+_0$ 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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J. Symbolic Logic, Volume 58, Issue 2 (1993), 557-578.

First available in Project Euclid: 6 July 2007

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Brown, Douglas K.; Simpson, Stephen G. The Baire Category Theorem in Weak Subsystems of Second-Order Arithmetic. J. Symbolic Logic 58 (1993), no. 2, 557--578.

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