Geodesic
On Isomorphisms of Relations Embedded into Each Other
Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 573-589

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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. 
@article{MZM_2003_74_4_a10,
     author = {D. I. Saveliev},
     title = {On {Isomorphisms} of {Relations} {Embedded} into {Each} {Other}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {573--589},
     publisher = {mathdoc},
     volume = {74},
     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a10/}
}
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D. I. Saveliev. On Isomorphisms of Relations Embedded into Each Other. Matematičeskie zametki, Tome 74 (2003) no. 4, pp. 573-589. http://geodesic.mathdoc.fr/item/MZM_2003_74_4_a10/