Multi-algebras from the viewpoint of algebraic logic

Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/46

Title:	Multi-algebras from the viewpoint of algebraic logic
Authors:	Cirulis, Janis
Keywords:	алгебра
Issue Date:	9-Oct-2002
Publisher:	Луганский национальный университет им. Т. Шевченко
Description:	Where U is a structure for a first-order language L¼ with equality ≈, a standard construction associates with every formula f of L¼ 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 L¼ 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 " of singular inclusion is accepted as the basic one (s"t 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 " tk. The class of such functions is given an axiomatic description.
URI:	http://hdl.handle.net/123456789/46
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