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Infinitary combinatorics and modal logic

Published online by Cambridge University Press:  12 March 2014

Andreas Blass
Andreas Blass*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
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Abstract

We show that the modal propositional logic G, originally introduced to describe the modality “it is provable that”, is also sound for various interpretations using filters on ordinal numbers, for example the end-segment filters, the club filters, or the ineffable filters. We also prove that G is complete for the interpretation using end-segment filters. In the case of club filters, we show that G is complete if Jensen's principle □κ holds for all κ < ℵω; on the other hand, it is consistent relative to a Mahlo cardinal that G be incomplete for the club filter interpretation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 761 - 778
Copyright
Copyright © Association for Symbolic Logic 1990

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