Pacific Journal of Mathematics

A unifying condition for implications among the axioms of choice for finite sets.

Martin M. Zuckerman

Article information

Source
Pacific J. Math., Volume 28, Number 1 (1969), 233-242.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102983625

Mathematical Reviews number (MathSciNet)
MR0239970

Zentralblatt MATH identifier
0177.01502

Subjects
Primary: 02.60
Secondary: 05.00

Citation

Zuckerman, Martin M. A unifying condition for implications among the axioms of choice for finite sets. Pacific J. Math. 28 (1969), no. 1, 233--242. https://projecteuclid.org/euclid.pjm/1102983625


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References

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  • [2] K. Gdel, Theconsistency of the axiom of choice andof the generalized continuum- hypothesis with the axioms of set theory, 6thed., Annals of Math. Studies 3, Princeton Univ. Press, Princeton,1964.
  • [3] A. Mostowski, Uber die Unabhangigkeit des Wohlordnungssatzes vom Ordnungs- princip, Fund. Math. 32 (1939), 201-252.
  • [4] A. Mostowski, Axiom of choice for finite sets, Fund. Math. 33 (1945), 137-168.
  • [5] W. Sierpinski, L'axiome du choix pour les ensembles finis, 10 (1955), 92-99.
  • [6] W. Sierpinski, Cardinal and ordinal numbers, 1st, ed., Monografe Matematyczne 34, Pastwome Wydawnictwo Naukowe, Warszawa,1958.
  • [7] W. Szmielew, On choices from finite sets, Fund. Math. 34 (1947), 75-80.
  • [8] P. L. Tchebychef, Oeuvres, tome 1, Publiees par les soins de A. Markoff and N. Sonin, Chelsea Publ. Co., New York, 1962.
  • [9] M. Zuckerman, Bertrand's Postulate and conditions (M) and (S) for the axiom of choice for finite sets (to appear in Illinois J. Math.).
  • [10] M. Zuckerman, Some theorems on the axiom of choice for finite sets (to appear in Z. Math. Logik Grundlagen Math.).
  • [12] M. Zuckerman, Finite versions of the axiom of choice, Ph. D. Thesis, Dept. of Math., Yeshiva University, New York (1967).