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Continuity, freeness, and filtrations. (English) Zbl 1242.03049
Summary: The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in incremental constructions of (standard) finitely generated free \(\mathbb{S}_4\)-algebras.

MSC:
03B45 Modal logic (including the logic of norms)
03B22 Abstract deductive systems
06E25 Boolean algebras with additional operations (diagonalizable algebras, etc.)
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