2023/08/25 by Bezhanishvili, Guram, Bezhanishvili, Nick, Lucero-Bryan, Joel +1
#03B45 #03E10 #03E50 #54D35 #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO)
paper · doi:10.48550/arxiv.2308.13684
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(ω2), 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.