Journal of Symbolic Logic

Topological Elementary Equivalence of Closed Semi-Algebraic Sets in the Real Plane

Bart Kuijpers, Jan Paredaens, and Jan Van Den Bussche

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Abstract

We investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

Article information

Source
J. Symbolic Logic, Volume 65, Issue 4 (2000), 1530-1555.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746251

Mathematical Reviews number (MathSciNet)
MR1812168

Zentralblatt MATH identifier
0974.03038

JSTOR
links.jstor.org

Citation

Kuijpers, Bart; Paredaens, Jan; Bussche, Jan Van Den. Topological Elementary Equivalence of Closed Semi-Algebraic Sets in the Real Plane. J. Symbolic Logic 65 (2000), no. 4, 1530--1555. https://projecteuclid.org/euclid.jsl/1183746251


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