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Łoś' theorem and the Boolean prime ideal theorem imply the axiom of choice


Author: Paul E. Howard
Journal: Proc. Amer. Math. Soc. 49 (1975), 426-428
MSC: Primary 02K20
DOI: https://doi.org/10.1090/S0002-9939-1975-0384548-X
MathSciNet review: 0384548
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Abstract: In this paper it is shown that Łoś' theorem and the Boolean prime ideal theorem imply the axiom of choice. The possibility of eliminating the use of the Boolean prime ideal theorem from the proof is also discussed.


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

  • [1] J. Łoś, Quelque remarques, théorèmes et problèmes sur les classes définissables d'algèbres, Mathematical Interpretation of Formal Systems, North-Holland, Amsterdam, 1955, pp. 98-113. MR 17, 700.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0384548-X
Keywords: Axiom of choice, Boolean prime ideal theorem, Łoś' theorem
Article copyright: © Copyright 1975 American Mathematical Society