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CHARACTERIZING EXISTENCE OF A MEASURABLE CARDINAL VIA MODAL LOGIC
Part of
GURAM BEZHANISHVILI, NICK BEZHANISHVILI, JOEL LUCERO-BRYAN, JAN VAN MILL
Journal:

The Journal of Symbolic Logic / Volume 86 / Issue 1 / March 2021

Published online by Cambridge University Press:

01 February 2021, pp. 162-177

Print publication:

March 2021
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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.

ON A PROBLEM OF TALAGRAND CONCERNING SEPARATELY CONTINUOUS FUNCTIONS
Part of
Volodymyr Mykhaylyuk, Roman Pol
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 5 / September 2021

Published online by Cambridge University Press:

06 February 2020, pp. 1719-1728

Print publication:

September 2021
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We construct a separately continuous function $e:E\times K\rightarrow \{0,1\}$ on the product of a Baire space $E$ and a compact space $K$ such that no restriction of $e$ to any non-meagre Borel set in $E\times K$ is continuous. The function $e$ has no points of joint continuity, and, hence, it provides a negative solution of Talagrand’s problem in Talagrand [Espaces de Baire et espaces de Namioka, Math. Ann.270 (1985), 159–164].