Publication
Title
Topological elementary equivalence of regular semi‐algebraic sets in three‐dimensional space
Author
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 transformations 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.
Language
English
Source (journal)
Mathematical logic quarterly. - Leipzig
Publication
Leipzig : Barth , 2018
ISSN
0942-5616 [print]
1521-3870 [online]
Volume/pages
64 :6 (2018) , p. 435-463
ISI
000454411500003
Full text (Publisher's DOI)
Full text (open access)
Full text (publisher's version - intranet only)
UAntwerpen
 Faculty/Department Research group Publication type Subject Affiliation Publications with a UAntwerp address