Topology and modality: The topological interpretation of first-order modal logic

Review of Symbolic Logic 1 (2):146-166 (2008)
As McKinsey and Tarski showed, the Stone representation theorem for Boolean algebras extends to algebras with operators to give topological semantics for (classical) propositional modal logic, in which the operation is modeled by taking the interior of an arbitrary subset of a topological space. In this article, the topological interpretation is extended in a natural way to arbitrary theories of full first-order logic. The resulting system of S4 first-order modal logic is complete with respect to such topological semantics
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DOI 10.1017/S1755020308080143
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Tamar Lando (2015). First Order S4 and its Measure-Theoretic Semantics. Annals of Pure and Applied Logic 166 (2):187-218.

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