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http://hdl.handle.net/1942/25875
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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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