- #3,026

- 95

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A sketch of how it works in this case is that certain logics have algebraic counterparts (usually based on Boolean algebras or lattices), and there are various ways, largely based on Stone and Priestley dualities, for interpreting these algebraic structures as topological spaces (possibly equipped with some extra structure, like the ordering in Priestley duality), and the maps between them as continuous functions (usually with additional properties) with domain and range switched. I know that these dualities have been used to prove completeness results for various logics, though I can't give details off the top of my head.