RUDN Journal of PhilosophyRUDN Journal of PhilosophyВестник Российского университета дружбы народов. Cерия: Философия2313-23022408-8900Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)11405ArticlesСтатьиResearch ArticleThe Review of Relations of Principles of Strong Uniformization and Church Thesis in Intuitionistic Set TheoryОбзор соотношений принципов униформизации и тезисов Чёрча в интуиционистской теории множествKhakhanianValery KhristoforovichХаханянВалерий ХристофоровичChair of Mathematicsvalkhakhanian@gmail.comMoscow State University of railway communicationsМосковский государственный университет путей сообщения150420134NO4 (2013)№4 (2013)475012092016Copyright ©; 2013, Khakhanian V.K.Copyright ©; 2013, Хаханян В.Х.2013Khakhanian V.K.Хаханян В.Х.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/philosophy/article/view/11405We prove that the strong uniformization does not depend on Church thesis with choice in the set theory with intuitionistic logic and with axiom of extensionality.В работе рассмотрены доказанные ранее в статьях автора и приведен (без доказательства) последний из результатов о соотношениях разных видов принципа униформизации и тезисов Чёрча в теории множеств с интуиционистской логикой.intuitionistic set theoryChurch thesisuniformizationMarkov principleтезис Черчя«сильная униформизация»интуиционистская логикааксиома объемности1.Khakhanian V.Kh. The independence principle of uniformization from Church thesis in intuitionistic set theory // Mathematical Note 43, issue 5 (may). — 1988. — P. 685—691 (Russian).2.Troelstra A.S. Notes on the intuitionistic second order arithmetic // Lecture Notes in Mathematics. — 1973. — N. 337. — P. 171—205.3.Khakhanian V.Kh. Set theory and Church thesis // The investigations by non classical logics and formal systems. — M.: Nauka, 1983. — P. 198—208 (Russian).4.Shwartz G. Some applications of method of recursive realizability to intuitionistic set types // Questions of cybernetics. Non classical logics and its applications. — M., 1982. — P. 37—54 (Russian).5.Khakhanian V.Kh. The consistency of intuitionistic set theory with principles of Church thesis and uniformization // Vestnik of Moscow State University. Serie “Mathematics and Mechanics”. — 1980. — N 5. — P. 3—7 (Russian).6.Khakhanian V.Kh. The independence of strong uniformization from Church thesis in full set theory // Scientific mathematical readings in commemoration of M.Y. Suslin. Saratov, 16—21, October, 1989. Abstracts SGPI, 1989. — P. 91 (Russian).7.Khakhanyan V.Kh. Independence of the uniformity principle from Church's thesis in intuitionistic set theory // Izvestia RAN. Ser. Mat. — 2013. — 77:6. — P. 209—224.