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STRONG COMPLETENESS OF MODAL LOGICS OVER 0-DIMENSIONAL METRIC SPACES

Published online by Cambridge University Press:  24 October 2019

ROBERT GOLDBLATT  and
IAN HODKINSON
ROBERT GOLDBLATT*
Affiliation:
School of Mathematics and Statistics, Victoria University of Wellington
IAN HODKINSON*
Affiliation:
Department of Computing, Imperial College London
*
*SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITY WELLINGTON, NEW ZEALAND E-mail: Rob.Goldblatt@msor.vuw.ac.nz
†DEPARTMENT OF COMPUTING IMPERIAL COLLEGE LONDON LONDON, UK E-mail: i.hodkinson@imperial.ac.uk
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Abstract

We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for some languages and spaces, no standard modal deductive system is strongly complete.

Keywords

Primary 03B45Secondary 54E35dense in itselfCantor setcoderivative operatoruniversal modalitydifference modalitygraded modalities
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 3 , September 2020 , pp. 611 - 632
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Copyright
Copyright © Association for Symbolic Logic 2019 

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