Advertisement

Notes on the theory of scales

  • Alexander S. Kechris
  • Yiannis N. Moschovakis
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 689)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. W. Addison, Some consequences of the axiom of constructibility, Fund. Math. 46 (1959a), 123–135.MathSciNetzbMATHGoogle Scholar
  2. [2]
    J. W. Addison and Yiannis N. Moschovakis, Some consequences of the axiom of definable determinateness, Proc. Nat. Acad. Sci. USA 59 (1968), 708–712.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Morton Davis, Infinite games of perfect information, Advances in game theory, Ann. of Math. Study No. 52, 1964, 85–101.MathSciNetzbMATHGoogle Scholar
  4. [4]
    K. Kuratowski, Topology v. 1, Academic Press, New York & London, 1966.zbMATHGoogle Scholar
  5. [5]
    A. Levy, Definability in axiomatic set theory: I, in Proc. 1964 International Congress for Logic, Methodology and Philosophy of Science, Amsterdam, 1966.Google Scholar
  6. [6]
    R. Mansfield, The theory of Σ21 sets, doctoral dissertation, Stanford University, 1969.Google Scholar
  7. [7]
    _____, Perfect subsets of definable sets of real numbers, Pacific Journal of Mathematics, (2) 35 (1970), 451–457.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    _____, A Souslin operation on π21, Israel Journal of Mathematics, (3) 9 (1971), 367–379.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    D. A. Martin, The axiom of determinateness and reduction principles in the analytical hierarchy, Bull. Amer. Math. Soc. 74 (1968), 687–689.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    _____, Pleasant and unpleasant consequences of determinateness, unpublished manuscript circulated in March 1970.Google Scholar
  11. [11]
    D. A. Martin and R. M. Solovay, A basis theorem for Σ31 sets of reals, Ann. of Math., 89 (1969), 138–160.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Yiannis N. Moschovakis, The Suslin-Kleene theorem for countable structures, Duke Math. Journal, (2) 37 (June 1970), 341–352.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    _____, Determinacy and prewellorderings of the continuum, Math Logic and Foundations of Set Theory, Edited by Y. Bar Hsillel, North Holland, Amsterdam-London, 1970, 24–62.Google Scholar
  14. [14]
    _____, Uniformization in a playful universe, Bull. Amer. Math. Soc., to appear.Google Scholar
  15. [15]
    _____, Descriptive set theory, a foundational approach, in preparation.Google Scholar
  16. [16]
    J. Mycielski, On the axiom of determinateness, Fund. Math., 53 (1964), 205–224.MathSciNetzbMATHGoogle Scholar
  17. [17]
    J. Mycielski and S. Swierczkowski, On the Lebesgue measurability and the axiom of determinateness, Fund. Math., 54 (1964), 67–71.MathSciNetzbMATHGoogle Scholar
  18. [18]
    Jack H. Silver, Measurable cardinals and Δ31 wellorderings, to appear.Google Scholar
  19. [19]
    R. M. Solovay, A model of set theory in which every set is Lebesgue measurable, Ann. of Math., 92 (1970), 1–56.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    _____, On the cardinality of Σ1/2 sets of reals, Foundations of Mathematics, Symposium papers commemorating the 60th birthday of Kurt Gödel, Springer-Verlag, 1966, 58–73.Google Scholar
  21. [21]
    R. M. Solovay, Measurable cardinals and the axiom of determinateness, Lecture notes prepared in connection with the Summer Institute on Axiomatic Set Theory held at UCIA, Summer 1967.Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Alexander S. Kechris
    • 1
  • Yiannis N. Moschovakis
    • 2
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadena
  2. 2.Department of MathematicsUniversity of CaliforniaLos Angeles

Personalised recommendations