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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/25875

Title: Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space
Authors: Kuijpers, Bart
Geerts, Floris
Issue Date: 2018
Citation: MATHEMATICAL LOGIC QUARTERLY,
Status: In Press
Abstract: We consider semi-algebraic sets and properties of these sets that are expressible by sentences in first-order logic over the reals. We are interested in first-order properties that are invariant under topological transforma- tions of the ambient space. Two semi-algebraic sets are called topologically elementarily equivalent if they cannot be distinguished by such topological first-order sentences. So far, only semi-algebraic sets in one and two-dimensional space have been considered in this context. Our contribution is a natural characterisation of topological elementary equivalence of regular closed semi-algebraic sets in three-dimensional space, extending a known characterisation for the two-dimensional case. Our characterisation is based on the local topological behaviour of semi-algebraic sets and the key observation that topologically elementarily equivalent sets can be transformed into each other by means of geometric transformations, each of them mapping a set to a first-order indistinguishable one.
URI: http://hdl.handle.net/1942/25875
ISSN: 0942-5616
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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