Abstract
Let \({\beta(\mathbb{N})}\) denote the Stone–Čech compactification of the set \({\mathbb{N}}\) of natural numbers (with the discrete topology), and let \({\mathbb{N}^\ast}\) denote the remainder \({\beta(\mathbb{N})-\mathbb{N}}\). We show that, interpreting modal diamond as the closure in a topological space, the modal logic of \({\mathbb{N}^\ast}\) is S4 and that the modal logic of \({\beta(\mathbb{N})}\) is S4.1.2.
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To the memory of Lazo Zambakhidze (1942–2008).
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Bezhanishvili, G., Harding, J. The modal logic of \({\beta(\mathbb{N})}\) . Arch. Math. Logic 48, 231–242 (2009). https://doi.org/10.1007/s00153-009-0123-9
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DOI: https://doi.org/10.1007/s00153-009-0123-9