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. - Berlin
Mathematical logic quarterly. - Berlin
Publication
Berlin : 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
External links
Web of Science
Record
Identification
Creation 10.01.2019
Last edited 23.09.2021
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