Completeness of the Gödel–Löb Provability Logic for the Filter Sequence of Normal Measures

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Journal of Symbolic Logic 89 (1):163-174 (2024)
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Abstract

Assuming the existence of suitable large cardinals, we show it is consistent that the Provability logic $\mathbf {GL}$ is complete with respect to the filter sequence of normal measures. This result answers a question of Andreas Blass from 1990 and a related question of Beklemishev and Joosten.

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10.1017/jsl.2023.8

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References found in this work

Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
Sets constructible from sequences of ultrafilters.William J. Mitchell - 1974 - Journal of Symbolic Logic 39 (1):57-66.
Topological completeness of the provability logic GLP.Lev Beklemishev & David Gabelaia - 2013 - Annals of Pure and Applied Logic 164 (12):1201-1223.
Infinitary combinatorics and modal logic.Andreas Blass - 1990 - Journal of Symbolic Logic 55 (2):761-778.

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