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

Samuel M. Corson

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arXiv · 2001.06513

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

Samuel M. Corson

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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.

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BibTeX RIS

Samuel M. Corson. 2020-01-17. The independence of Stone's Theorem from the Boolean Prime Ideal Theorem. https://arxiv.org/abs/2001.06513

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