## The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem

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- by Samuel M. Corson
- Proc. Amer. Math. Soc.
**148**(2020), 5381-5386 - DOI: https://doi.org/10.1090/proc/15164
- Published electronically: September 18, 2020
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## 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.## References

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## Bibliographic 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
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 5381-5386 - MSC (2010): Primary 03E25, 54A35, 54E35, 54D20
- DOI: https://doi.org/10.1090/proc/15164
- MathSciNet review: 4163849