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Topological elementary equivalence of closed semi-algebraic sets in the real plane

Published online by Cambridge University Press:  12 March 2014

Bart Kuijpers ,
Jan Paredaens  and
Jan Van den Bussche
Bart Kuijpers
Affiliation:
Department Wni, University of Limburg(LUC), Universitaire Campus, B-3590 Diepenbeek, Belgium, E-mail:bart.kuijpers@luc.ac.be
Jan Paredaens
Affiliation:
Department of Mathematics and Computer Science, University of Antwerp(UIA), Universiteitsplein 1, B-2610 Antwerp, Belgium, E-mail:pareda@uia.ua.ac.be
Jan Van den Bussche
Affiliation:
Department Wni, University of Limburg(LUC), Universitaire Campus, B-3590 Diepenbeek, Belgium, E-mail:vdbuss@luc.ac.be
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 4 , December 2000 , pp. 1530 - 1555
Copyright
Copyright © Association for Symbolic Logic 2000

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