INCLUSION CRITERIA
An entry belongs in this subdivision if and only if its subject is a correspondence between a class of algebras and a class of spaces or relational structures, or the machinery that transports a logic's structure across such a correspondence.
Required: At least one of the following:
- A representation or duality theorem between a variety of algebras and a category of topological or relational structures (Stone, Priestley, Esakia, Jónsson–Tarski)
- A construction carrying an algebraic semantics to a relational one or back (canonical extension, complex algebra, ultrafilter frame, general and descriptive frames)
- A transfer result whose content is what the duality preserves (canonicity, correspondence, modal definability)
Not sufficient: An algebraic semantics presented on its own (Algebraic, where the logic lives; Model-Theory for the study of algebraizability as such). A relational semantics presented on its own (Modal). A categorical formulation of a logic (Categorical)—a duality is an equivalence of categories, but the subject here is which two categories and what the equivalence preserves, not the category theory that states it.
Boundary: Sahlqvist correspondence and the Goldblatt–Thomason theorem are duality results; their statements are about modal formulas and frames and are cross-listed with Modal, while the duality that proves them lives here. Abstract algebraic logic asks whether a logic has an algebraic semantics at all and belongs in Model-Theory; this subdivision asks what that semantics is dual to. Stone duality's categorical generalizations are cross-listed with Categorical.