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Proceedings of the American Mathematical Society

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Cardinals $ m$ such that $ 2m=m$

Authors: J. D. Halpern and Paul E. Howard
Journal: Proc. Amer. Math. Soc. 26 (1970), 487-490
MSC: Primary 02.60
MathSciNet review: 0268034
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Abstract: In this paper we compare characterizations of cardinals $ m$ satisfying $ 2 \cdot m = m$ with certain characterizations of Dedekind infinite cadinals. It is also shown that a strengthening of $ \forall m$ ($ m$ an infinite cardinal $ \Rightarrow 2 \cdot m = m$) implies the axiom of choice.

References [Enhancements On Off] (What's this?)

  • [1] J. D. Halpern, The independence of the axiom of choice from the Boolean prime ideal theorem, Fund. Math. 55 (1964), 57–66. MR 0164891,
  • [2] Azriel Lévy, The Fraenkel-Mostowski method for independence proofs, Internat. Sympos. Theory of Models (Berkeley, Calif., 1963) North-Holland, Amsterdam, 1965, pp. 221-228. MR 34 #1166.
  • [3] Wacław Sierpiński, Cardinal and ordinal numbers, 2nd ed., Monografie Mat., Tom 34, PWN, Warsaw, 1958. MR 20 #2288.

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Keywords: Axiom of choice, cardinal, Dedekind infinite cardinals, cardinal arithmetic
Article copyright: © Copyright 1970 American Mathematical Society

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