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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.
We obtain a simple construction for particular subclasses of several varieties of lattice expansions. The construction allows a unified approach to the characterization of the subdirectly irreducible algebras
Basic concepts concerning binary and ternary relations are extended to relations of arbitrary arities and then investigated.
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