Number of polynomials in dependence preserving algebras
Fraïssé introduced the notion of a -set-homogeneous relational structure. In the present paper the following classes of monounary algebras are described: , , —the class of all algebras which are 2-set-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively, and , , —the class of all algebras which are 2-homogeneous with respect to subalgebras, connected subalgebras, connected partial subalgebras, respectively.
In this paper we investigate the validity of a cancellation law for some classes of monounary algebras.
Basic concepts concerning binary and ternary relations are extended to relations of arbitrary arities and then investigated.