### 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.