Multi-algebras from the viewpoint of algebraic logic

Where U is a structure for a first-order language L ≈ with equality ≈, a standard construction associates with every formula f of L ≈ the set kfk of those assignments which fulfill f in U. These sets make up a (cylindric like) set algebra Cs(U) that is a homomorphic image of the algebra of for...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2003
1. Verfasser: Cırulis, J.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2003
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/154670
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Multi-algebras from the viewpoint of algebraic logic / J. Cırulis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 20–31. — Бібліогр.: 17 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-154670
record_format dspace
spelling Cırulis, J.
2019-06-15T17:37:46Z
2019-06-15T17:37:46Z
2003
Multi-algebras from the viewpoint of algebraic logic / J. Cırulis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 20–31. — Бібліогр.: 17 назв. — англ.
1726-3255
2001 Mathematics Subject Classification: 08A99; 03G15, 08A62.
https://nasplib.isofts.kiev.ua/handle/123456789/154670
Where U is a structure for a first-order language L ≈ with equality ≈, a standard construction associates with every formula f of L ≈ the set kfk of those assignments which fulfill f in U. These sets make up a (cylindric like) set algebra Cs(U) that is a homomorphic image of the algebra of formulas. If L ≈ does not have predicate symbols distinct from ≈, i.e. U is an ordinary algebra, then Cs(U) is generated by its elements ks ≈ tk; thus, the function (s, t) 7→ ks ≈ tk comprises all information on Cs(U). In the paper, we consider the analogues of such functions for multi-algebras. Instead of ≈, the relation ε of singular inclusion is accepted as the basic one (sεt is read as ‘s has a single value, which is also a value of t’). Then every multi-algebra U can be completely restored from the function (s, t) 7→ ks ε tk. The class of such functions is given an axiomatic description.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Multi-algebras from the viewpoint of algebraic logic
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Multi-algebras from the viewpoint of algebraic logic
spellingShingle Multi-algebras from the viewpoint of algebraic logic
Cırulis, J.
title_short Multi-algebras from the viewpoint of algebraic logic
title_full Multi-algebras from the viewpoint of algebraic logic
title_fullStr Multi-algebras from the viewpoint of algebraic logic
title_full_unstemmed Multi-algebras from the viewpoint of algebraic logic
title_sort multi-algebras from the viewpoint of algebraic logic
author Cırulis, J.
author_facet Cırulis, J.
publishDate 2003
language English
container_title Algebra and Discrete Mathematics
publisher Інститут прикладної математики і механіки НАН України
format Article
description Where U is a structure for a first-order language L ≈ with equality ≈, a standard construction associates with every formula f of L ≈ the set kfk of those assignments which fulfill f in U. These sets make up a (cylindric like) set algebra Cs(U) that is a homomorphic image of the algebra of formulas. If L ≈ does not have predicate symbols distinct from ≈, i.e. U is an ordinary algebra, then Cs(U) is generated by its elements ks ≈ tk; thus, the function (s, t) 7→ ks ≈ tk comprises all information on Cs(U). In the paper, we consider the analogues of such functions for multi-algebras. Instead of ≈, the relation ε of singular inclusion is accepted as the basic one (sεt is read as ‘s has a single value, which is also a value of t’). Then every multi-algebra U can be completely restored from the function (s, t) 7→ ks ε tk. The class of such functions is given an axiomatic description.
issn 1726-3255
url https://nasplib.isofts.kiev.ua/handle/123456789/154670
citation_txt Multi-algebras from the viewpoint of algebraic logic / J. Cırulis // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 1. — С. 20–31. — Бібліогр.: 17 назв. — англ.
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