Literature Cited
S. S. Kutateladze, “Convex operators,” Usp. Mat. Nauk,34, No. 1, 167–196 (1979).
A. M. Rubinov, “Sublinear operators and their applications,” Usp. Mat. Nauk,32, No. 4, 113–174 (1977).
A. G. Kusraev and S. S. Kutateladze, “Local convex analysis,” in: Current Problems of Mathematics [in Russian], Vol. 19, VINITI, Moscow (1982), pp. 155–206.
T. J. Jech, “Lectures in set theory with particular emphasis on the method of forcing,” Lect. Notes Math.,217, Springer-Verlag, Berlin-New York (1971).
Yu. I. Manin, Provable and Unprovable [in Russian], Sov. Radio, Moscow (1979).
S. S. Kutateladze, “The Krein-Mil'man theorem and its generalization,” Sib. Mat. Zh.,21, No. 1, 130–138 (1980).
S. S. Kutateladze, “On convex analysis in modules,” Sib. Mat. Zh.,22, No. 4, 118–128 (1981).
A. G. Kusraev, Some Applications of the Theory of Boolean-Velued Models in Functional Analysis [in Russian], Preprint, No. 5, Inst. Mat. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1982).
E. I. Gordon, “K-spaces in Boolean-valued models of set theory,” Dokl. Akad. Nauk SSSR,258, No. 4, 777–780 (1981).
I. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory, Clarendon Press, Oxford (1979).
G. Takeuti and W. Zaring, Axiomatic Set Theory, Springer-Verlag, Berlin-New York (1973).
G. Takeuti, Two Applications of Logic to Mathematics, Iwanami, Tokyo (1978).
E. I. Gordon, “Real numbers in the Boolean-valued models of set theory and K-spaces,” Dokl. Akad. Nauk SSSR,237, No. 4, 773–775 (1977).
E. I. Gordon, “On the theorems of preservation of relations in K-spaces,” Sib. Mat. Zh.,23, No. 5, 55–65 (1982).
A. G. Kusraev and S. S. Kutateladze, “Analysis of subdifferentials with the help of Boolean-valued models,” Dokl. Akad. Nauk SSSR,265, No. 5, 1061–1064 (1982).
B. Z. Vulikh, Introduction to the Theory of Partially Ordered Vector Spaces [in Russian], Gosudarstvennoe Izd. Fizikomatematicheskoi Literatury, Moscow (1961).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 24, No. 5, pp. 109–122, September–October, 1983.
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Kusraev, A.G., Kutateladze, S.S. Subdifferentials in Boolean-valued models of set theory. Sib Math J 24, 735–746 (1983). https://doi.org/10.1007/BF00969600
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DOI: https://doi.org/10.1007/BF00969600