Geodesic
A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 4, pp. 543-546.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.14712/1213-7243.2015.138
Classification : 03E25, 03E35, 03E40, 03E45
Keywords: Boolean Prime Ideal Theorem; the Axiom of Choice 
@article{10_14712_1213_7243_2015_138,
     author = {Repick\'y, Miroslav},
     title = {A proof of the independence of the {Axiom} of {Choice} from the {Boolean} {Prime} {Ideal} {Theorem}},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {543--546},
     publisher = {mathdoc},
     volume = {56},
     number = {4},
     year = {2015},
     doi = {10.14712/1213-7243.2015.138},
     mrnumber = {3434228},
     zbl = {06537723},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.138/}
}
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
SP  - 543
EP  - 546
VL  - 56
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.138/
DO  - 10.14712/1213-7243.2015.138
LA  - en
ID  - 10_14712_1213_7243_2015_138
ER  - 
%0 Journal Article
%A Repický, Miroslav
%T A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem
%J Commentationes Mathematicae Universitatis Carolinae
%D 2015
%P 543-546
%V 56
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.138/
%R 10.14712/1213-7243.2015.138
%G en
%F 10_14712_1213_7243_2015_138
Repický, Miroslav. A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 4, pp. 543-546. doi : 10.14712/1213-7243.2015.138. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.138/

Cité par Sources :