THE REVIEW OF RELATIONS OF PRINCIPLES OF STRONG UNIFORMIZATION AND CHURCH THESIS IN INTUITIONISTIC SET THEORY Valery Kh. <...> Khakhanian Chair of Mathematics Moscow State University of railway communications ul. <...> Obraztsova, 9, stroenie 9, GSP-4, Moscow, Russia, 127994 We 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. <...> In [1] was proved the independence of the principle of the strong uniformization on Church thesis with choice in the intuitionistic set theory with two kinds of variables, without extesionality plus the strong Markov principle and double complement of sets (DCS). <...> This principle appeared for the first time in the work of A. Troelstra [2] for the second order arithmetic with variable on sets of natural numbers variables. <...> Forms of Church thesis which are examined in the present work (with choice — strong thesis CT and with uniqueness — CT!) and strong Markov principle are well known and can be found in [3]. <...> We give an additional formulation of the classical true principle DCS, which has in our double kinds language the following notation: ∀a∃x[∀n(¬¬n∈a→n∈x)∧∀u(¬¬u∈a→u∈x)]. <...> In [3] we used a model in which all axiom schemes and axioms of the set theory and all above mentioned principles are realized excepting the uniformization that it was not possible to realize and its realization was not disproved. <...> The problem of investigations of relations of principles U, U!, CT, CT! on the level of the set theory is connected above all with the proof of nonderivability of principles of uniformization from principles of Church and determination of the role of extensionality in the second case. <...> In the end of my work I will give the summary of results for the set theories of ZF-type with intuitionistic logic including the result which is obtained in the present work. <...> We note also that for the intuitionistic type theory corresponding results were obtained by G. Scwartz in [4] and in the same work the role of extensionality was explained. 47 Вестник РУДН, серия Философия, 2013, № 4 In the present work we announce the nonderivability of the strong uniformization in the intuitionistic set theory with two kinds of variables and extensionality (full set theory!) and additional Markov strong principle, DCS <...>