Topological Elementary Equivalence of Closed Semi-Algebraic Sets in the Real Plane
Bart Kuijpers, Jan Paredaens, and Jan Van Den Bussche
Source: J. Symbolic Logic Volume 65, Issue 4
(2000), 1530-1555.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183746251
JSTOR: links.jstor.org
Mathematical Reviews number (MathSciNet): MR1812168
Zentralblatt MATH identifier: 0974.03038
