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DC Field | Value | Language |
---|---|---|
dc.contributor.author | GEERTS, Floris | - |
dc.contributor.author | KUIJPERS, Bart | - |
dc.date.accessioned | 2018-04-12T12:27:36Z | - |
dc.date.available | 2018-04-12T12:27:36Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | MATHEMATICAL LOGIC QUARTERLY, 64 (6), p. 435-463. | - |
dc.identifier.issn | 0942-5616 | - |
dc.identifier.uri | http://hdl.handle.net/1942/25875 | - |
dc.description.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. | - |
dc.language.iso | en | - |
dc.rights | © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim | - |
dc.subject.other | spatial logics; first-order logic over the reals; topological elementary equivalence | - |
dc.title | Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 463 | - |
dc.identifier.issue | 6 | - |
dc.identifier.spage | 435 | - |
dc.identifier.volume | 64 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Kuijpers, B (reprint author), Univ Hasselt, Databases & Theoret Comp Sci Res Grp, Agoralaan, B-3590 Diepenbeek, Belgium. bart.kuijpers@uhasselt.be | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.doi | 10.1002/malq.201800017 | - |
dc.identifier.isi | 000454411500003 | - |
item.fullcitation | GEERTS, Floris & KUIJPERS, Bart (2018) Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space. In: MATHEMATICAL LOGIC QUARTERLY, 64 (6), p. 435-463.. | - |
item.fulltext | With Fulltext | - |
item.contributor | GEERTS, Floris | - |
item.contributor | KUIJPERS, Bart | - |
item.accessRights | Open Access | - |
crisitem.journal.issn | 0942-5616 | - |
crisitem.journal.eissn | 1521-3870 | - |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
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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