Journal of Symbolic Logic

Located Sets and Reverse Mathematics

Mariagnese Giusto and Stephen G. Simpson

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Abstract

Let X be a compact metric space. A closed set K $\subseteq$ X is located if the distance function d(x, K) exists as a continuous real-valued function on X; weakly located if the predicate d(x, K) $>$ r is $\Sigma^0_1$ allowing parameters. The purpose of this paper is to explore the concepts of located and weakly located subsets of a compact separable metric space in the context of subsystems of second order arithmetic such as RCA$_0$, WKL$_0$ and ACA$_0$. We also give some applications of these concepts by discussing some versions of the Tietze extension theorem. In particular we prove an RCA$_0$ version of this result for weakly located closed sets.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 3 (2000), 1451-1480.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746189

Mathematical Reviews number (MathSciNet)
MR1791384

Zentralblatt MATH identifier
0967.03051

JSTOR
links.jstor.org

Citation

Giusto, Mariagnese; Simpson, Stephen G. Located Sets and Reverse Mathematics. J. Symbolic Logic 65 (2000), no. 3, 1451--1480. https://projecteuclid.org/euclid.jsl/1183746189


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