Quantifiers on distributive lattices

DOI10.1016/0012-365X(91)90312-PzbMath0753.06012MaRDI QIDQ1185078

Roberto L. O. Cignoli

Publication date: 28 June 1992

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

varietyPriestley spacesubdirectly irreducible algebrasbounded distributive latticesnon-Boolean analogue of a quantifier

Mathematics Subject Classification ID

Lattices of varieties (08B15) Cylindric and polyadic algebras; relation algebras (03G15) Subdirect products and subdirect irreducibility (08B26) Distributive lattices (06D99)

Related Items (30)

Quasivarities of distributive lattices with a quantifier ⋮ Universal varieties of quasi-Stone algebras ⋮ A preliminary study of MV-algebras with two quantifiers which commute ⋮ Monadic \(k\times j\)-rough Heyting algebras ⋮ Free \(Q\)-distributive lattices ⋮ Distributive lattices with an operator ⋮ The logic Ł^• ⋮ Equations in the theory of \(Q\)-distributive lattices ⋮ An infinity of super-Belnap logics ⋮ Bounded lattice structured discriminator varieties ⋮ ENDOMORPHISMS OF DISTRIBUTIVE LATTICES WITH A QUANTIFIER ⋮ An alternative definition of quantifiers on four-valued Łukasiewicz algebras ⋮ Monadic quasi-modal distributive nearlattices ⋮ A topological duality for monadic MV-algebras ⋮ Coproducts of distributive lattice-based algebras. ⋮ Simple and subdirectly irreducibles bounded distributive lattices with unary operators ⋮ Topological spaces of monadic MV-algebras ⋮ Varieties of quasi-Stone algebras ⋮ Linear Heyting algebras with a quantifier ⋮ Bounded lattice expansions ⋮ On a definition of a variety of monadic \(\ell\)-groups. ⋮ XI Latin American Symposium on Mathematical Logic ⋮ Dual binary discriminator varieties ⋮ Weak-quasi-Stone algebras ⋮ An algebraic study of S5-modal Gödel logic ⋮ On monadic operators on modal pseudocomplemented De Morgan algebras and tetravalent modal algebras ⋮ Topological representation for monadic implication algebras ⋮ Quasi-modal operators on distributive nearlattices ⋮ Hilbert algebras with a modal operator \(\diamondsuit\) ⋮ Distributive Lattices with a Negation Operator

Cites Work

• Convergence of quantifiers and martingales
• Algèbres de Boole monadiques libres
• Quantifiers and orthomodular lattices
• Quantifier theory on quasi-orthomodular lattices
• Ordered Topological Spaces and the Representation of Distributive Lattices
• Boolean multiplicative closures, I
• Algebras Whose Congruence Lattices are Distributive.
• Representation of Distributive Lattices by means of ordered Stone Spaces
• On Equational Classes of Algebraic Versions of Logic I.
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