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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.)
##### Keywords:
filtrations; free algebras; modal logic
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##### References:
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