Modal languages for topology: Expressivity and definability

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Abstract

In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem characterization theorem and the Goldblatt–Thomason definability theorem in terms of the well-established first-order topological language Lt.

MSC

03B48
54A05
03C40

Keywords

Modal logic
Topology
Expressivity
Definability

Cited by (0)

The authors wish to thank Yde Venema for posing the question of modal definability for topological spaces, and for his invaluable help and guidance in establishing one of the main results of the present paper: the algebraic proof of the topological Goldblatt–Thomason theorem presented in Section 4, which first appeared in the MSc thesis of the second author [D. Gabelaia, Modal definability in topology, Master’s Thesis, University of Amsterdam, 2001], written under Yde’s supervision. The other results and techniques we present here can be seen as a continuation of the same project, completing the picture in a wider setting. The work of the first author was supported by the Netherlands Organization for Scientific Research (NWO) grant 639.021.508. The work of the second author was supported by INTAS grant Nr. 1-04-77-7080 and by the Georgian National Science Foundation grants GNSF/ST06/3-003 and GNSF/ST06/3-017.