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Title: | Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space | Authors: | GEERTS, Floris KUIJPERS, Bart |
Issue Date: | 2018 | Source: | MATHEMATICAL LOGIC QUARTERLY, 64 (6), p. 435-463. | 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. | Notes: | Kuijpers, B (reprint author), Univ Hasselt, Databases & Theoret Comp Sci Res Grp, Agoralaan, B-3590 Diepenbeek, Belgium. bart.kuijpers@uhasselt.be | Keywords: | spatial logics; first-order logic over the reals; topological elementary equivalence | Document URI: | http://hdl.handle.net/1942/25875 | ISSN: | 0942-5616 | e-ISSN: | 1521-3870 | DOI: | 10.1002/malq.201800017 | ISI #: | 000454411500003 | Rights: | © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim | Category: | A1 | Type: | Journal Contribution |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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3d-tee.pdf | Peer-reviewed author version | 1.34 MB | Adobe PDF | View/Open |
Geerts_et_al-2018-Mathematical_Logic_Quarterly.pdf Restricted Access | Published version | 2.36 MB | Adobe PDF | View/Open Request a copy |
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