The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem
Author:
Samuel M. Corson
Journal:
Proc. Amer. Math. Soc. 148 (2020), 5381-5386
MSC (2010):
Primary 03E25, 54A35, 54E35, 54D20
DOI:
https://doi.org/10.1090/proc/15164
Published electronically:
September 18, 2020
MathSciNet review:
4163849
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Abstract | References | Similar Articles | Additional Information
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.
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Additional Information
Samuel M. Corson
Affiliation:
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, 28049 Madrid, Spain
MR Author ID:
1133429
ORCID:
0000-0003-0050-2724
Email:
sammyc973@gmail.com
Keywords:
Paracompact,
metacompact,
metric space,
Boolean Prime Ideal Theorem
Received by editor(s):
February 17, 2020
Received by editor(s) in revised form:
April 9, 2020, April 14, 2020, and April 15, 2020
Published electronically:
September 18, 2020
Additional Notes:
This work was supported by ERC grant PCG-336983 and by the Severo Ochoa Programme for Centres of Excellence in R&D SEV-20150554.
Communicated by:
Heike Mildenberger
Article copyright:
© Copyright 2020
American Mathematical Society
