Modal Logic of Generalized Separated Topological Spaces
Authors: Qian Chen and Minghui Ma
Published in: Logic and Its Applications, ICLA 2023, LNCS 13963, 92–104. DOI: https://doi.org/10.1007/978-3-031-26689-8_7
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Abstract
For each non-zero cardinal $\kappa$, this paper introduces a generalized separation axiom $T_0^\kappa$ for topological spaces. For every integer $n>0$, under $\mathsf{d}$-semantics interpreting $\Diamond$ as the derived set operator, the class of all $T_0^n$-spaces is $\mathsf{d}$-defined by the modal formula $\mathrm{t}_0^n$, and $\mathsf{wK4T}_0^n=\mathsf{wK4}\oplus \mathrm{t}_0^n$ is the $\mathsf{d}$-logic of all $T_0^n$-spaces. For $\kappa\geq\aleph_0$, the class of all $T_0^\kappa$-spaces is not $\mathsf{d}$-definable.
