On the intuitive set theory and its formalization
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2008), pp. 3-12
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The present paper investigates the reasons of occurrence of known paradoxes in the intuitive set theory. We have proved that the process of formation of sets is non-finishing, and the reason of occurrence of paradoxes consists in representation of formation of sets as a finishing process (in other words, the reason of occurrence of paradoxes is the identification of concepts of a set and a class). The possibility of full formalization of the intuitive set theory is suspected.
@article{UZERU_2008_2_a0,
author = {I. G. Khachatryan},
title = {On the intuitive set theory and its formalization},
journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
pages = {3--12},
year = {2008},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZERU_2008_2_a0/}
}
I. G. Khachatryan. On the intuitive set theory and its formalization. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2008), pp. 3-12. http://geodesic.mathdoc.fr/item/UZERU_2008_2_a0/
[1] S. K.Klini, Vvedenie v metamatematiku, IL, M., 1957
[2] S. K. Klini, Matematicheskaya logika, Mir, M., 1973
[3] Kh. B. Karri, Osnovaniya matematicheskoi logiki, Mir, M., 1969
[4] И. П. Натансон Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974
[5] N. Burbaki, Teoriya mnozhestv, Mir, M., 1965
[6] Dzh. Shenfild, Matematicheskaya logika, Nauka, M., 1975
[7] К. Куратовский, А. Мостовский Teoriya mnozhestv, Mir, M., 1970
[8] T. Iekh, Teoriya mnozhestv i metod forsinga, Mir, M., 1973
[9] P. Dzh. Koen, Teoriya mnozhestv i kontinuum-gipoteza, Mir, M., 1969
[10] Dzh. L. Kelli, Obschaya topologiya, Nauka, M., 1968
[11] P. Kon, Universalnaya algebra, Mir, M., 1968