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CHARACTERIZING EXISTENCE OF A MEASURABLE CARDINAL VIA MODAL LOGIC

Part of: Set theory General logic Fairly general properties Peculiar spaces

Published online by Cambridge University Press:  01 February 2021

GURAM BEZHANISHVILI ,
NICK BEZHANISHVILI ,
JOEL LUCERO-BRYAN  and
JAN VAN MILL
GURAM BEZHANISHVILI
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES NEW MEXICO STATE UNIVERSITYLAS CRUCES, NM, USA E-mail:guram@nmsu.edu
NICK BEZHANISHVILI
Affiliation:
INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITY OF AMSTERDAMAMSTERDAM, THE NETHERLANDS E-mail:N.Bezhanishvili@uva.nl
JOEL LUCERO-BRYAN
Affiliation:
DEPARTMENT OF MATHEMATICS KHALIFA UNIVERSITY OF SCIENCE AND TECHNOLOGYABU DHABI, UNITED ARAB EMIRATES E-mail:joel.bryan@ku.ac.ae
JAN VAN MILL
Affiliation:
KORTEWEG-DE VRIES INSTITUTE FOR MATHEMATICS UNIVERSITY OF AMSTERDAMAMSTERDAM, THE NETHERLANDS E-mail:j.vanMill@uva.nl
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Abstract

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We prove that the existence of a measurable cardinal is equivalent to the existence of a normal space whose modal logic coincides with the modal logic of the Kripke frame isomorphic to the powerset of a two element set.

Keywords

modal logictopological semanticsmeasurable cardinalnormal spaceextremally disconnected spacescattered space

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03E55: Large cardinals 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) 54G05: Extremally disconnected spaces, $F$-spaces, etc. 54G12: Scattered spaces
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 1 , March 2021 , pp. 162 - 177
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Copyright
© The Association for Symbolic Logic 2021

References

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