Israel Journal of Mathematics

, Volume 20, Issue 2, pp 149–163

A model of ZF with an infinite free complete Boolean algebra

  • Jonathan Stavi
Article

Abstract

By a theorem of Gaifman and Hales no model of ZF+AC (Zermelo-Fraenkel set theory plus the axiom of choice) contains an infinite free complete Boolean algebra. We construct a model of ZF in which an infinite free c.B.a. exists.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Gaifman,Infinite Boolean polynomials I, Fund. Math.54 (1964), 229–250.MathSciNetGoogle Scholar
  2. 2.
    J. Gregory,Incompleteness of a formal system for infinitary finite-quantifier formulas, J. Symbolic Logic36 (1971), 445–455.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    A. W. Hales,On the non-existence of free complete Boolean algebras, Fund, Math.54 (1964), 45–66.MATHMathSciNetGoogle Scholar
  4. 4.
    T. J. Jech,The Axiom of Choice, North-Holland, Amsterdam (American Elsevier-New York), 1973.MATHGoogle Scholar
  5. 5.
    C. R. Karp,Languages with Expressions of Infinite Length, Nort-Holland, Amsterdam, 1964.MATHGoogle Scholar
  6. 6.
    S. Kripke,An extension of a theorem of Gaifman-Hales-Solovay, Fund. Math.61 (1967), 29–32.MATHMathSciNetGoogle Scholar
  7. 7.
    A. Levy,A hierarchy of formulas in set theory, Mem. Amer. Math. Soc.57 (1965).Google Scholar
  8. 8.
    R. M. Solovay,New proof of a theorem of Gaifman and Hales, Bull. Amer. Math. Soc.72 (1966), 282–284.MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    J. Stavi,On strongly and weakly defined Boolean terms, Israel J. Math.15 (1973), 31–43.MATHMathSciNetGoogle Scholar
  10. 10.
    J. Stavi,Extensions of Kripke’s embedding theorem, to appear in Ann. Math. Logic.Google Scholar
  11. 11.
    J. Stavi,Free complete Boolean algebras and first order structures, Notices Amer. Math. Soc.22 (1975), A-326.Google Scholar

Copyright information

© The Weizmann Science Press of Israel 1975

Authors and Affiliations

  • Jonathan Stavi
    • 1
    • 2
  1. 1.The Hebrew University of JerusalemJerusalemIsrael
  2. 2.Stanford UniversityStanfordU.S.A.

Personalised recommendations