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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/23448

Title: Topological elementary equivalence of regular semi-algebraic sets in three-dimensional space
Authors: Geerts, Floris
Kuijpers, Bart
Issue Date: 2016
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.
Notes: Ingediend bij het tijdschrift Proceedings of the London Mathematical Society, December 2016.
URI: http://hdl.handle.net/1942/23448
Category: R2
Type: Research Report
Appears in Collections: Research publications

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