Multi-algebras from the viewpoint of algebraic logic
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Multi-algebras from the viewpoint of algebraic logic
|
|
| Creator |
Cırulis, J.
|
|
| 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. |
|
| Date |
2019-06-15T17:37:46Z
2019-06-15T17:37:46Z 2003 |
|
| Type |
Article
|
|
| Identifier |
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 |
|
| Language |
en
|
|
| Relation |
Algebra and Discrete Mathematics
|
|
| Publisher |
Інститут прикладної математики і механіки НАН України
|
|