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The independence of Stone's Theorem from the Boolean Prime Ideal Theorem.
- Source :
-
Proceedings of the American Mathematical Society . Dec2020, Vol. 148 Issue 12, p5381-5386. 6p. - Publication Year :
- 2020
-
Abstract
- We give a permutation model in which Stone's theorem (every metric space is paracompact) is false and the Boolean Prime Ideal Theorem (every ideal in a Boolean algebra extends to a prime ideal) is true. The erring metric space in our model attains only rational distances and is not metacompact. Transfer theorems give the comparable independence in the Zermelo-Fraenkel setting, answering a question of Good, Tree, and Watson. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 148
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 146510594
- Full Text :
- https://doi.org/10.1090/proc/15164