On Isomorphisms of Relations Embedded into Each Other

In this paper, we consider analogs of the Cantor--Bernstein theorem for sets with binary relations. In Sec. 1, we prove an analog of this theorem for arbitrary binary relations; in Sec. 2, we consider an application; in Sec. 3, we study a class of relations with the “Cantor-- Bernstein property” and a class of exact relations, and prove that these classes are closed under certain operations.