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COMPLETENESS OF THE GÖDEL–LÖB PROVABILITY LOGIC FOR THE FILTER SEQUENCE OF NORMAL MEASURES

Part of: Set theory Proof theory and constructive mathematics

Published online by Cambridge University Press:  23 February 2023

MOHAMMAD GOLSHANI Open the ORCID record for MOHAMMAD GOLSHANI [Opens in a new window]  and
REIHANE ZOGHIFARD
MOHAMMAD GOLSHANI*
Affiliation:
SCHOOL OF MATHEMATICS INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM) TEHRAN, 19395-5746, IRAN E-mail: r.zoghi@gmail.com
REIHANE ZOGHIFARD
Affiliation:
SCHOOL OF MATHEMATICS INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM) TEHRAN, 19395-5746, IRAN E-mail: r.zoghi@gmail.com
*
E-mail: golshani.m@gmail.com
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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.

Keywords

provability logicmeasurable cardinalnormal measure

MSC classification

Primary: 03E35: Consistency and independence results 03E55: Large cardinals 03F45: Provability logics and related algebras (e.g., diagonalizable algebras)

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 1 , March 2024 , pp. 163 - 174
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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