{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:35:07Z","timestamp":1747150507288,"version":"3.40.5"},"reference-count":31,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T00:00:00Z","timestamp":1543795200000},"content-version":"vor","delay-in-days":2,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider semi\u2010algebraic sets and properties of these sets that are expressible by sentences in first\u2010order logic over the reals. We are interested in first\u2010order properties that are invariant under topological transformations of the ambient space. Two semi\u2010algebraic sets are called <jats:italic>topologically elementarily equivalent<\/jats:italic> if they cannot be distinguished by such topological first\u2010order sentences. So far, only semi\u2010algebraic sets in one and two\u2010dimensional space have been considered in this context. Our contribution is a natural characterisation of topological elementary equivalence of regular closed semi\u2010algebraic sets in three\u2010dimensional space, extending a known characterisation for the two\u2010dimensional case. Our characterisation is based on the local topological behaviour of semi\u2010algebraic 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\u2010order indistinguishable one.<\/jats:p>","DOI":"10.1002\/malq.201800017","type":"journal-article","created":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T16:16:36Z","timestamp":1543853796000},"page":"435-463","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topological elementary equivalence of regular semi\u2010algebraic sets in three\u2010dimensional space"],"prefix":"10.1002","volume":"64","author":[{"given":"Floris","family":"Geerts","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science Universiteit Antwerpen Middelheimlaan 1 Antwerpen 2020 Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5774-0948","authenticated-orcid":false,"given":"Bart","family":"Kuijpers","sequence":"additional","affiliation":[{"name":"Databases and Theoretical Computer Science Research Group Universiteit Hasselt &amp; Transnationale Universiteit Limburg Agoralaan, Gebouw D Diepenbeek 3590 Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,12,3]]},"reference":[{"volume-title":"The Knot Book, An Elementary Introduction to the Mathematical Theory of Knots","year":"1994","author":"Adams C. 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