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arXiv:2001.06513 [math.LO]AbstractReferencesReviewsResources

The independence of Stone's Theorem from the Boolean Prime Ideal Theorem

Samuel M. Corson

Published 2020-01-17Version 1

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.

Categories: math.LO
Subjects: 03E25, 54A35, 54E35, 54D20
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