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&#...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2003 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2003
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154670 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862712477704257536 |
|---|---|
| author | Cırulis, J. |
| author_facet | Cırulis, J. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T17:37:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-154670 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:37:16Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| 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 |
| spellingShingle | Multi-algebras from the viewpoint of algebraic logic Cırulis, J. |
| title | 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_short | Multi-algebras from the viewpoint of algebraic logic |
| title_sort | multi-algebras from the viewpoint of algebraic logic |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154670 |
| work_keys_str_mv | AT cırulisj multialgebrasfromtheviewpointofalgebraiclogic |