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arXiv · 2308.13684

On Shehtman's Two Problems

Guram Bezhanishvili·Nick Bezhanishvili·Joel Lucero-Bryan·Jan van Mill
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Abstract

We provide partial solutions to two problems posed by Shehtman concerning the modal logic of the Čech-Stone compactification of an ordinal space. We use the Continuum Hypothesis to give a finite axiomatization of the modal logic of $β(ω^2)$, thus resolving Shehtman's first problem for $n=2$. We also characterize modal logics arising from the Čech-Stone compactification of an ordinal $γ$ provided the Cantor normal form of $γ$ satisfies an additional condition. This gives a partial solution of Shehtman's second problem.

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Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan, Jan van Mill. 2023-08-25. On Shehtman's Two Problems. https://arxiv.org/abs/2308.13684

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