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

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: Journal
• Year: 2000
• Where: JSYML
• Authors: Bart Kuijpers, Jan Paredaens, Jan Van den Bussche
• Keywords: Binary Relation Symbol, First-order Logic Sentences, JSYML 2000, Topological Properties