A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
Commentationes Mathematicae Universitatis Carolinae (2015)
- Volume: 56, Issue: 4, page 543-546
- ISSN: 0010-2628
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topRepický, Miroslav. "A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem." Commentationes Mathematicae Universitatis Carolinae 56.4 (2015): 543-546. <http://eudml.org/doc/276214>.
@article{Repický2015,
abstract = {We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.},
author = {Repický, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Boolean Prime Ideal Theorem; the Axiom of Choice},
language = {eng},
number = {4},
pages = {543-546},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem},
url = {http://eudml.org/doc/276214},
volume = {56},
year = {2015},
}
TY - JOUR
AU - Repický, Miroslav
TI - A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 4
SP - 543
EP - 546
AB - We present a proof of the Boolean Prime Ideal Theorem in a transitive model of ZF in which the Axiom of Choice does not hold. We omit the argument based on the full Halpern-Läuchli partition theorem and instead we reduce the proof to its elementary case.
LA - eng
KW - Boolean Prime Ideal Theorem; the Axiom of Choice
UR - http://eudml.org/doc/276214
ER -
References
top- Halpern J.D., Läuchli H., 10.1090/S0002-9947-1966-0200172-2, Trans. Amer. Math. Soc. 124 (1966), 360–367. Zbl0158.26902MR0200172DOI10.1090/S0002-9947-1966-0200172-2
- Halpern J.D., Lévy A., The Boolean Prime Ideal Theorem does not imply the Axiom of Choice, In: Axiomatic Set Theory, Proceedings of Symposia in Pure Mathematics, vol. XIII, Part I, pp. 83–134, AMS, Providence, 1971. Zbl0233.02024MR0284328
- Jech T., Set Theory, Academic Press, New York-London, 1978. Zbl1007.03002MR0506523
- Jech T., Set Theory, the third millennium edition, revised and expanded, Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl1007.03002MR1940513
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