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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todo:paper_0012365X_v96_n3_p183_Cignoli2023-10-03T14:10:22Z Quantifiers on distributive lattices Cignoli, R. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0012365X_v96_n3_p183_Cignoli |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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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. |
| format |
JOUR |
| author |
Cignoli, R. |
| spellingShingle |
Cignoli, R. Quantifiers on distributive lattices |
| author_facet |
Cignoli, R. |
| author_sort |
Cignoli, R. |
| title |
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 |
| url |
http://hdl.handle.net/20.500.12110/paper_0012365X_v96_n3_p183_Cignoli |
| work_keys_str_mv |
AT cignolir quantifiersondistributivelattices |
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1782024627402309632 |