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Splittings and the finite model property

Published online by Cambridge University Press:  12 March 2014

Marcus Kracht
Marcus Kracht*
Affiliation:
II. Department of Mathematics, 1000 Berlin 33, Germany, E-mail: kracht@math.fu-berlin.de
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Abstract

An old conjecture of modal logics states that every splitting of the major systems K4, S4, G and Grz has the finite model property. In this paper we will prove that all iterated splittings of G have fmp, whereas in the other cases we will give explicit counterexamples. We also introduce a proof technique which will give a positive answer for large classes of splitting frames. The proof works by establishing a rather strong property of these splitting frames namely that they preserve the finite model property in the following sense. Whenever an extension Λ has fmp so does the splitting Λ/f of Λ by f. Although we will also see that this method has its limitations because there are frames lacking this property, it has several desirable side effects. For example, properties such as compactness, decidability and others can be shown to be preserved in a similar way and effective bounds for the size of models can be given. Moreover, all methods and proofs are constructive.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 139 - 157
Copyright
Copyright © Association for Symbolic Logic 1993

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References

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