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http://hdl.handle.net/1942/23448
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DC Field | Value | Language |
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dc.contributor.author | GEERTS, Floris | - |
dc.contributor.author | KUIJPERS, Bart | - |
dc.date.accessioned | 2017-04-06T14:40:28Z | - |
dc.date.available | 2017-04-06T14:40:28Z | - |
dc.date.issued | 2016 | - |
dc.identifier.uri | http://hdl.handle.net/1942/23448 | - |
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 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. | - |
dc.language.iso | en | - |
dc.rights | Gelieve niet publiek toegankelijk te maken! | - |
dc.subject.other | Semi-algebraic sets; first-order logic | - |
dc.title | Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space | - |
dc.type | Research Report | - |
local.format.pages | 33 | - |
local.bibliographicCitation.jcat | R2 | - |
dc.description.notes | Ingediend bij het tijdschrift Proceedings of the London Mathematical Society, December 2016. | - |
local.type.specified | Research Report | - |
item.fulltext | With Fulltext | - |
item.fullcitation | GEERTS, Floris & KUIJPERS, Bart (2016) Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space. | - |
item.accessRights | Closed Access | - |
item.contributor | GEERTS, Floris | - |
item.contributor | KUIJPERS, Bart | - |
Appears in Collections: | Research publications |
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