MacNeille completions and canonical extensions

DOI10.1090/S0002-9947-05-03816-XzbMath1083.06009OpenAlexW1508875804MaRDI QIDQ5705523

Mai Gehrke, John Harding, Yde Venema

Publication date: 9 November 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03816-x

zbMATH Keywords

MacNeille completionBoolean algebras with operatorscanonical extensionmonotone bounded lattice expansions

Mathematics Subject Classification ID

Complete lattices, completions (06B23) Boolean algebras with additional operations (diagonalizable algebras, etc.) (06E25) Varieties of lattices (06B20)

Related Items (22)

Subcompletions of representable relation algebras ⋮ Generalized Kripke frames ⋮ Lewis meets Brouwer: constructive strict implication ⋮ Intermediate logics admitting a structural hypersequent calculus ⋮ Algebraic proof theory for substructural logics: cut-elimination and completions ⋮ Topological duality and algebraic completions ⋮ Canonical extensions of posets. ⋮ On canonicity and completions of weakly representable relation algebras ⋮ Dedekind–MacNeille completion and Cartesian product of multi-adjoint lattices ⋮ On the logic of belief and propositional quantification ⋮ MacNeille transferability and stable classes of Heyting algebras ⋮ Canonical extensions: an algebraic approach to Stone duality ⋮ Preservation of Sahlqvist fixed point equations in completions of relativized fixed point Boolean algebras with operators ⋮ Correspondence, canonicity, and model theory for monotonic modal logics ⋮ On two fragments with negation and without implication of the logic of residuated lattices ⋮ Definable operators on stable set lattices ⋮ Completion and finite embeddability property for residuated ordered algebras. ⋮ Canonical extensions and ultraproducts of polarities ⋮ On the variety generated by completions of representable relation algebras ⋮ Comparison of MacNeille, canonical, and profinite completions ⋮ Modal languages for topology: expressivity and definability ⋮ Hyper-MacNeille completions of Heyting algebras

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