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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0268034-9
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.
- J. D. Halpern, The independence of the axiom of choice from the Boolean prime ideal theorem, Fund. Math. 55 (1964), 57–66. MR 164891, DOI https://doi.org/10.4064/fm-55-1-57-66 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. 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