Infinitary combinatorics and modal logic

Journal of Symbolic Logic 55 (2):761-778 (1990)

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 $\kappa ; on the other hand, it is consistent relative to a Mahlo cardinal that G be incomplete for the club filter interpretation
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DOI 10.2307/2274663
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References found in this work BETA

The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Pure and Applied Logic 4 (3):229.
Strong Axioms of Infinity and Elementary Embeddings.R. M. SolovÀy - 1978 - Annals of Pure and Applied Logic 13 (1):73.
Some Exact Equiconsistency Results in Set Theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
The Unprovability of Consistency. An Essay in Modal Logic.George Boolos - 1979 - Journal of Symbolic Logic 46 (4):871-873.
Set Theory.Thomas Jech - 1981 - Journal of Symbolic Logic 46 (4):876-877.

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Citations of this work BETA

Topological Completeness of the Provability Logic GLP.Lev Beklemishev & David Gabelaia - 2013 - Annals of Pure and Applied Logic 164 (12):1201-1223.
Intuitionistic Logic and Modality Via Topology.Leo Esakia - 2004 - Annals of Pure and Applied Logic 127 (1-3):155-170.
The Polytopologies of Transfinite Provability Logic.David Fernández-Duque - 2014 - Archive for Mathematical Logic 53 (3-4):385-431.

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