Topological elementary equivalence of closed semi-algebraic sets in the real plane
Bart Kuijpers, Jan Paredaens, Jan Van den Bussche · Journal of Symbolic Logic · 2000
Abstract We investigate topological properties of subsetsSof the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol forS. 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.