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Order-continuous functionals in Boolean-valued models of set theory

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Literature Cited

  1. D. Maharam, “The representation of abstract integrals,” Trans. Am. Math. Soc.,75, 154–184 (1953).

    Google Scholar 

  2. D. Maharam, “On kernel representation of linear operators,” Trans. Am. Math. Soc.,79, 299–355 (1955).

    Google Scholar 

  3. W. A. I. Luxemburg and A. R. Schep, “A Radon-Nikodym type theorem for positive operators of a dual,” Indag. Math.,81, No. 3, 357–375 (1978).

    Google Scholar 

  4. A. g. Kusraev, “A generalization of the disintegration formula,” Dokl. Akad. Nauk SSSR,265, No. 6, 1312–1316 (1982).

    Google Scholar 

  5. 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).

    Google Scholar 

  6. T. J. Jech, Lectures in Set Theory with Particular Emphasis on the Method of Forcing, Lecture Notes in Math., Vol. 217, Springer-Verlag, Berlin-New York (1971).

    Google Scholar 

  7. G. Takeuti and W. M. Zaring, Axiomatic Set Theory, Springer-Verlag, Berlin-New York (1973).

    Google Scholar 

  8. J. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory, Clarendon Press, Oxford (1977).

    Google Scholar 

  9. R. M. Solovay and S. Tennenbaum, “Iterated Cohen extensions and Souslin's problem,” Ann. Math.,94, No. 2, 201–245 (1971).

    Google Scholar 

  10. B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Gordon and Breach (1967).

  11. G. P. Akilov and S. S. Kutateladze, Ordered Vector Spaces [in Russian], Nauka, Novosibirsk (1978).

    Google Scholar 

  12. E. I. Gordon, “K-Spaces in Boolean-valued models of set theory,” Dokl. Akad. Nauk SSSr,258, No. 4, 777–780 (1981).

    Google Scholar 

  13. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  14. C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lect. Notes Math., Vol. 580, Springer-Verlag, Berlin-New York (1977).

    Google Scholar 

  15. B. Z. Vulikh and G. Ya. Lozanovskii, “On the representation of completely linear and regular functionals in partially ordered spaces,” Mat. Sb.,84, No. 3, 331–352 (1971).

    Google Scholar 

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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 1, pp. 69–79, January–February, 1984.

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Kusraev, A.G. Order-continuous functionals in Boolean-valued models of set theory. Sib Math J 25, 57–65 (1984). https://doi.org/10.1007/BF00969509

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  • DOI: https://doi.org/10.1007/BF00969509

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