Canonical extensions of posets.

DOI10.1007/s00012-014-0292-1zbMath1302.06002OpenAlexW2009663113MaRDI QIDQ466925

Wilmari Morton

Publication date: 31 October 2014

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00012-014-0292-1

zbMATH Keywords

canonical extensionsextensions of mapsfilters of posetsposet extensions

Mathematics Subject Classification ID

Partial orders, general (06A06) Complete lattices, completions (06B23) Other algebras related to logic (03G25) Algebraic aspects of posets (06A11) Galois correspondences, closure operators (in relation to ordered sets) (06A15)

Related Items

Distributive and completely distributive lattice extensions of ordered sets ⋮ Amalgamating poset extensions and generating free lattices ⋮ Coalgebraic Completeness-via-Canonicity ⋮ A spectral-style duality for distributive posets ⋮ Canonical extensions and ultraproducts of polarities ⋮ Embedding ordered sets into distributive lattices ⋮ Unnamed Item ⋮ The free distributive semilattice extension of a distributive poset

Cites Work

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• Relational semantics for full linear logic
• Canonical extensions for congruential logics with the deduction theorem
• On canonicity of poset expansions
• A completion for partially ordered Abelian groups
• On profinite completions and canonical extensions
• Residuated lattices. An algebraic glimpse at substructural logics
• Completion and finite embeddability property for residuated ordered algebras.
• Ideals in ordered sets, a unifying approach
• Standard completions for quasiordered sets
• A universal mapping property for a lattice completion
• On the canonicity of Sahlqvist identities
• Constructive canonicity in non-classical logics
• \(\Delta_1\)-completions of a poset.
• Existence of prime ideals and ultrafilters in partially ordered sets
• Completions of Partially Ordered Sets
• The Completion of a Partially Ordered Set with Respect to a Polarization
• MacNeille completions and canonical extensions
• Canonical extensions and relational completeness of some substructural logics
• Boolean Algebras with Operators. Part I
• Boolean Algebras with Operators
• Ideals in Partially Ordered Sets
• Bounded lattice expansions