Notre Dame Journal of Formal Logic

Baire Categoricity and Σ10-Induction

Stephen G. Simpson

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 20 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1390246439

Digital Object Identifier
doi:10.1215/00294527-2377887

Mathematical Reviews number (MathSciNet)
MR3161413

Zentralblatt MATH identifier
1331.03017

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

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

Citation

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. https://projecteuclid.org/euclid.ndjfl/1390246439


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References

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  • [2] Fernandes, A. M., “The Baire category theorem over a feasible base theory,” pp. 164–74 in Reverse Mathematics 2001, edited by S. G. Simpson, vol. 21 of Lecture Notes in Logic, Association for Symbolic Logic, La Jolla, Calif., 2005.
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