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

Citation
B. Kuijpers et al., Topological elementary equivalence of closed semi-algebraic sets in the real plane, J SYMB LOG, 65(4), 2000, pp. 1530-1555
Citations number
23
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF SYMBOLIC LOGIC
ISSN journal
00224812 → ACNP
Volume
65
Issue
4
Year of publication
2000
Pages
1530 - 1555
Database
ISI
SICI code
0022-4812(200012)65:4<1530:TEEOCS>2.0.ZU;2-2
Abstract
We investigate topological properties of subsets S of the real plane, expre ssed bq first-order logic sentences in the language of the reals augmented with a binary relation symbol for S.. Two sets are called topologically ele mentary equivalent if they have the same such first-order topological prope rties. The contribution of this paper is a natural and effective characteri zation of topological elementary equivalence of closed semi-algebraic sets.