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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| Дата: | 2003 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2003
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154670 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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 |
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irk-123456789-1546702019-06-16T01:32:01Z Multi-algebras from the viewpoint of algebraic logic Cırulis, J. 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. 2003 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/154670 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cırulis, J. |
| spellingShingle |
Cırulis, J. Multi-algebras from the viewpoint of algebraic logic Algebra and Discrete Mathematics |
| author_facet |
Cırulis, J. |
| author_sort |
Cırulis, J. |
| title |
Multi-algebras from the viewpoint of algebraic logic |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2003 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT cırulisj multialgebrasfromtheviewpointofalgebraiclogic |
| first_indexed |
2023-05-20T17:45:12Z |
| last_indexed |
2023-05-20T17:45:12Z |
| _version_ |
1796154009091833856 |