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March 2012 Expansions which introduce no new open sets
Gareth Boxall, Philipp Hieromyni
J. Symbolic Logic 77(1): 111-121 (March 2012). DOI: 10.2178/jsl/1327068694

Abstract

We consider the question of when an expansion of a first-order topological structure has the property that every open set definable in the expansion is definable in the original structure. This question has been investigated by Dolich, Miller and Steinhorn in the setting of ordered structures as part of their work on the property of having o-minimal open core. We answer the question in a fairly general setting and provide conditions which in practice are often easy to check. We give a further characterisation in the special case of an expansion by a generic predicate.

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Gareth Boxall. Philipp Hieromyni. "Expansions which introduce no new open sets." J. Symbolic Logic 77 (1) 111 - 121, March 2012. https://doi.org/10.2178/jsl/1327068694

Information

Published: March 2012
First available in Project Euclid: 20 January 2012

zbMATH: 1245.03059
MathSciNet: MR2951632
Digital Object Identifier: 10.2178/jsl/1327068694

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 1 • March 2012
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