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Expansions which introduce no new open sets

Published online by Cambridge University Press:  12 March 2014

Gareth Boxall  and
Philipp Hieronymi
Gareth Boxall
Affiliation:
Department of Mathematical Sciences, Stellenbosch University, Stellenbosch 7600, South Africa, E-mail: [email protected]
Philipp Hieronymi
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 W. Green Street, Urbana, IL 61801, USA, E-mail: [email protected]
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 1 , March 2012 , pp. 111 - 121
Copyright
Copyright © Association for Symbolic Logic 2012

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