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. 
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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/

[1] Kuratovskii K., Mostovskii A., Teoriya mnozhestv, Mir, M., 1970

[2] Tarski A., Ordinal Algebras, Amsterdam, 1956

[3] Tarski A., Cardinal Algebras, Oxford University Press, NY, 1949 | Zbl

[4] Dedekind R., Gesammelte mathematische Werke, Braunschweig, 1932 | Zbl

[5] Rosenstein J. G., Linear orderings, NY, 1982

[6] Sierpiński W., Cardinal and Ordinal Numbers, Warsaw, 1958

[7] Jónsson B., Appendix B to: Tarski A., Ordinal Algebras, Amsterdam, 1956 | Zbl

[8] Savelev D. I., “Samopodobnye lineino uporyadochennye mnozhestva” (to appear) | Zbl

[9] Ginsburg S., “Some remarks on order types and decompositions of sets”, Trans. Amer. Math. Soc., 74:3 (1953), 514–535 | DOI | MR | Zbl

[10] Ginsburg S., “Further results on order types and decompositions of sets”, Trans. Amer. Math. Soc., 77:1 (1954), 122–150 | DOI | MR

[11] Ginsburg S., “Fixed points of products and ordered sums of simply ordered sets”, Proc. Amer. Math. Soc., 5:4 (1954), 554–565 | DOI | MR | Zbl

[12] Ginsburg S., “Order types and similarity transformations”, Trans. Amer. Math. Soc., 79:2 (1955), 341–361 | DOI | MR | Zbl

[13] Savelev D. I., “O poryadkovykh tipakh mnozhestv deistvitelnykh chisel” (to appear) | Zbl

[14] Gillman L., “A continuous exact set”, Proc. Amer. Math. Soc., 9:3 (1958), 412–418 | DOI | MR | Zbl

[15] Sherrie N., “Continuous and exact sets of specified cardinality”, Zeit. Math. Log. Grundlag. Math., 35 (1989), 211–224 | DOI | MR

[16] Lévy A., Basic Set Theory, Jerusalem, 1978

[17] Lindenbaum A., Tarski A., “Communication sur les recherches de la théorie des ensembles”, C. R. Sci. Varsovie, III, 19 (1926), 299–330