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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. 1 Introduction and summary By viewing subsets of ... (Update)
Context of citations to this paper: More
.... ( x 1 ; y 1 ) x 2 ; y 2 ) of S 1 (p; for a detailed description of the expression of this relation in FO Poly we refer to [10]) a) p p (b) Figure 4: The 1 environment of a database around p (a) and the construction to determine an p environment (smaller dashed...
...in Figure 1. In the next sections, we will use the following property (for a proof in the case of closed spatial databases we refer to [12]) Lemma 6. Let A be a spatial database. i) only a finite number of cone types appear in A; ii) A can only have infinitely many points of...
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4: A Decision Method for Elementary Algebra and Geometry (context) - Tarski - 1951
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BibTeX entry: (Update)
B. Kuijpers, J. Paredaens, and J. Van den Bussche. Topological elementary equivalence of closed semi-algebraic sets in the real plane. The Journal of Symbolic Logic, to appear, 1999. http://citeseer.comp.nus.edu.sg/123798.html More
@misc{ kuijpers99topological,
author = "B. Kuijpers and J. Paredaens and J. Van den Bussche",
title = "Topological elementary equivalence of closed semi-algebraic sets in the
real plane",
text = "B. Kuijpers, J. Paredaens, and J. Van den Bussche. Topological elementary
equivalence of closed semi-algebraic sets in the real plane. The Journal
of Symbolic Logic, to appear, 1999.",
year = "1999",
url = "citeseer.comp.nus.edu.sg/123798.html" }
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