## Notre Dame Journal of Formal Logic

### Baire Categoricity and $\Sigma^{0}_{1}$-Induction

Stephen G. Simpson

#### Abstract

We investigate the reverse-mathematical status of a version of the Baire category theorem known as $\mathrm {BCT}$. In a 1993 paper Brown and Simpson showed that $\mathrm {BCT}$ is provable in $\mathsf {RCA}_{0}$. We now show that $\mathrm {BCT}$ is equivalent to $\mathsf {RCA}_{0}$ over $\mathsf {RCA}_{0}^{{\ast }}$.

#### Article information

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

Dates
First available in Project Euclid: 20 January 2014

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

Digital Object Identifier
doi:10.1215/00294527-2377887

Mathematical Reviews number (MathSciNet)
MR3161413

Zentralblatt MATH identifier
1331.03017

#### 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

#### 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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