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CHARACTERIZING EXISTENCE OF A MEASURABLE CARDINAL VIA MODAL LOGIC

Published online by Cambridge University Press:  01 February 2021

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

Abstract

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.

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Article
Copyright
© The Association for Symbolic Logic 2021

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CHARACTERIZING EXISTENCE OF A MEASURABLE CARDINAL VIA MODAL LOGIC
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