Quantifiers on distributive lattices

A Q-distributive lattice is an algebra 〈L, ∧, ∨, ∇, 0, 1〉 of type (2, 2, 1, 0, 0) such that 〈L, ∧, ∨, 0, 1〉 is a bounded distributive lattice and ∇ satisfies the equations: (1) ∇0 = 0, (2) x ∧ ∇x = x, (3) ∇(x ∧ ∇y) = ∇x ∧ ∇y and (4) ∇(x ∨ y) = ∇x ∨ ∇y. The opposite of the category of Q-distributive...

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Publicado: 1991
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v96_n3_p183_Cignoli
http://hdl.handle.net/20.500.12110/paper_0012365X_v96_n3_p183_Cignoli
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_0012365X_v96_n3_p183_Cignoli2023-06-08T14:35:24Z Quantifiers on distributive lattices A Q-distributive lattice is an algebra 〈L, ∧, ∨, ∇, 0, 1〉 of type (2, 2, 1, 0, 0) such that 〈L, ∧, ∨, 0, 1〉 is a bounded distributive lattice and ∇ satisfies the equations: (1) ∇0 = 0, (2) x ∧ ∇x = x, (3) ∇(x ∧ ∇y) = ∇x ∧ ∇y and (4) ∇(x ∨ y) = ∇x ∨ ∇y. The opposite of the category of Q-distributive lattices is described in terms of Priestly spaces endowed with an equivalence relation. The simple and the sub-directly irreducible Q-distributive lattices are determined and it is shown that the lattices of equational classes of Q-distributive lattices is a chain of type ω + 1. © 1991. 1991 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v96_n3_p183_Cignoli http://hdl.handle.net/20.500.12110/paper_0012365X_v96_n3_p183_Cignoli
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description A Q-distributive lattice is an algebra 〈L, ∧, ∨, ∇, 0, 1〉 of type (2, 2, 1, 0, 0) such that 〈L, ∧, ∨, 0, 1〉 is a bounded distributive lattice and ∇ satisfies the equations: (1) ∇0 = 0, (2) x ∧ ∇x = x, (3) ∇(x ∧ ∇y) = ∇x ∧ ∇y and (4) ∇(x ∨ y) = ∇x ∨ ∇y. The opposite of the category of Q-distributive lattices is described in terms of Priestly spaces endowed with an equivalence relation. The simple and the sub-directly irreducible Q-distributive lattices are determined and it is shown that the lattices of equational classes of Q-distributive lattices is a chain of type ω + 1. © 1991.
title Quantifiers on distributive lattices
spellingShingle Quantifiers on distributive lattices
title_short Quantifiers on distributive lattices
title_full Quantifiers on distributive lattices
title_fullStr Quantifiers on distributive lattices
title_full_unstemmed Quantifiers on distributive lattices
title_sort quantifiers on distributive lattices
publishDate 1991
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0012365X_v96_n3_p183_Cignoli
http://hdl.handle.net/20.500.12110/paper_0012365X_v96_n3_p183_Cignoli
_version_ 1768546096722739200

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