Advertisement

Siberian Mathematical Journal

, Volume 25, Issue 1, pp 57–65 | Cite as

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

  • A. G. Kusraev
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    D. Maharam, “The representation of abstract integrals,” Trans. Am. Math. Soc.,75, 154–184 (1953).Google Scholar
  2. 2.
    D. Maharam, “On kernel representation of linear operators,” Trans. Am. Math. Soc.,79, 299–355 (1955).Google Scholar
  3. 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. 4.
    A. g. Kusraev, “A generalization of the disintegration formula,” Dokl. Akad. Nauk SSSR,265, No. 6, 1312–1316 (1982).Google Scholar
  5. 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. 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. 7.
    G. Takeuti and W. M. Zaring, Axiomatic Set Theory, Springer-Verlag, Berlin-New York (1973).Google Scholar
  8. 8.
    J. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory, Clarendon Press, Oxford (1977).Google Scholar
  9. 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. 10.
    B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Gordon and Breach (1967).Google Scholar
  11. 11.
    G. P. Akilov and S. S. Kutateladze, Ordered Vector Spaces [in Russian], Nauka, Novosibirsk (1978).Google Scholar
  12. 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. 13.
    A. D. Ioffe and V. M. Tikhomirov, Theory of Extremal Problems [in Russian], Nauka, Moscow (1974).Google Scholar
  14. 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. 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

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • A. G. Kusraev

There are no affiliations available

Personalised recommendations