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

Journal of Symbolic Logic 65 (4):1530-1555 (2000)
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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