| Title:
|
A proof of the independence of the Axiom of Choice from the Boolean Prime Ideal Theorem (English) |
| Author:
|
Repický, Miroslav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
543-546 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Boolean Prime Ideal Theorem |
| Keyword:
|
the Axiom of Choice |
| MSC:
|
03E25 |
| MSC:
|
03E35 |
| MSC:
|
03E40 |
| MSC:
|
03E45 |
| idZBL:
|
Zbl 06537723 |
| idMR:
|
MR3434228 |
| DOI:
|
10.14712/1213-7243.2015.138 |
| . |
| Date available:
|
2015-12-17T11:53:21Z |
| Last updated:
|
2018-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144758 |
| . |
| Reference:
|
[1] Halpern J.D., Läuchli H.: A partition theorem.Trans. Amer. Math. Soc. 124 (1966), 360–367. Zbl 0158.26902, MR 0200172, 10.1090/S0002-9947-1966-0200172-2 |
| Reference:
|
[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. Zbl 0233.02024, MR 0284328 |
| Reference:
|
[3] Jech T.: Set Theory.Academic Press, New York-London, 1978. Zbl 1007.03002, MR 0506523 |
| Reference:
|
[4] Jech T.: Set Theory.the third millennium edition, revised and expanded, Springer Monographs in Mathematics, Springer, Berlin, 2003. Zbl 1007.03002, MR 1940513 |
| . |
