README⤓ .txt 2026-07-17T121634.146 000000000000760 The correspondences between algebraic and relational semantics, and the machinery that transports structure across them. Stone's theorem makes Boolean algebras and Stone spaces two views of one thing; Jónsson and Tarski extend it to Boolean algebras with operators and descriptive frames, which is why modal logic has both an algebraic and a Kripke semantics and why the canonical model construction works; Esakia does the same for Heyting algebras and intermediate logics.
Canonical Extensions⤓ .md 2026-07-17T120407.600 000000000000864 Implicit in Jónsson and Tarski (1951–52) as the complex algebra of the ultrafilter frame; isolated and generalized by Mai Gehrke and Bjarni Jónsson, "Bounded distributive lattices with operators" (1994) and "Bounded distributive lattice expansions" (2004). Gehrke, Nagahashi, and Venema (2005) gave the Sahlqvist theory algebraically. The point of the generalization: canonicity is not about Boolean algebras or about modal logic, and stating it without either shows what it is about.
Esakia Duality⤓ .md 2026-07-17T120407.600 000000000000808 Leo Esakia, "Topological Kripke models" (1974), which gave the duality for Heyting algebras; the Blok–Esakia theorem (Blok 1976, Esakia 1976) is its most consequential corollary. Esakia's Heyting Algebras: Duality Theory was published in English only in 2019, forty-five years after the Russian original, which is part of why the subject was slow to travel.
Jonsson-Tarski Duality⤓ .md 2026-07-17T120407.600 000000000000840 Bjarni Jónsson and Alfred Tarski, "Boolean algebras with operators, Parts I and II" (American Journal of Mathematics, 1951–52) — written before Kripke semantics existed, and containing it. Goldblatt's "Metamathematics of modal logic" (1976) and Thomason's work made the connection explicit; Blackburn, de Rijke, and Venema's Modal Logic (2001) is where the field learned to teach it.
Sahlqvist Correspondence⤓ .md 2026-07-15T064852.000 000000000015928 Henrik Sahlqvist (1975). Modal formulas with first-order correspondents. Syntactic class guaranteeing correspondence. Canonical frame validity. Automatic axiomatization.
Stone Duality⤓ .md 2026-07-17T120407.600 000000000000800 Marshall Stone, "The theory of representations for Boolean algebras" (1936) and "Applications of the theory of Boolean rings to general topology" (1937). Priestley extended it to bounded distributive lattices (1970). The theorem that made "algebra and topology are the same subject twice" a working method rather than a slogan.
CRITERIA⤓ .txt 2026-07-17T120407.600 000000000000776 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.