Notre Dame Journal of Formal Logic

Baire Categoricity and Σ10-Induction

Stephen G. Simpson

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We investigate the reverse-mathematical status of a version of the Baire category theorem known as BCT. In a 1993 paper Brown and Simpson showed that BCT is provable in RCA0. We now show that BCT is equivalent to RCA0 over RCA0.

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Notre Dame J. Formal Logic, Volume 55, Number 1 (2014), 75-78.

First available in Project Euclid: 20 January 2014

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Zentralblatt MATH identifier

Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]
Secondary: 03F25: Relative consistency and interpretations 54E52: Baire category, Baire spaces

reverse mathematics second-order arithmetic Baire category theorem $\mathsf{RCA}_{0}$ $\mathsf{RCA} _{0}^{\ast}$ $\Sigma^{0}_{1}$-induction


Simpson, Stephen G. Baire Categoricity and $\Sigma^{0}_{1}$ -Induction. Notre Dame J. Formal Logic 55 (2014), no. 1, 75--78. doi:10.1215/00294527-2377887.

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