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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.
In this note we deal with a question concerning monounary algebras which is analogous to an open problem for partially ordered sets proposed by Duffus and Rival.
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