## Notre Dame Journal of Formal Logic

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

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

#### 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

**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