Geodesic
Foundations of a new axiomatic set theory
Izvestiya. Mathematics, Tome 37 (1991) no. 2, pp. 467-473 
A. M. Vdovin. Foundations of a new axiomatic set theory. Izvestiya. Mathematics, Tome 37 (1991) no. 2, pp. 467-473. http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a11/
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     title = {Foundations of a new axiomatic set theory},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1991_37_2_a11/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new axiomatic set theory, consisting of four axioms, is presented. In this theory one can prove as theorems all of the axioms of Zermelo–Fraenkel set theory with the axiom of choice (ZFC), except for the axiom of regularity.

[1] Gilbert D., Bernais P., Osnovaniya matematiki, t. 1, 2, Nauka, M., 1979 | MR

[2] Karri X., Osnovaniya matematicheskoi logiki, Mir, M., 1969

[3] Kolmogorov A. N., Dragalin A. G., Matematicheskaya logika. Dopolnitelnye glavy, MGU, M., 1984

[4] Koen L. Dzh., Teoriya mnozhestv i kontinuum-gipoteza, Mir, M., 1969 | MR

[5] Lindon R., Zametki po logike, Mir, M., 1968 | MR