The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem,Proceedings of the American Mathematical Society

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The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-09-18 , DOI: 10.1090/proc/15164
Samuel M. Corson

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.

中文翻译：

斯通定理与布尔素理想定理的独立性

摘要：我们给出一个排列模型，其中斯通定理（每个度量空间都是超紧致）是假的，布尔素数理想理想定理（布尔代数中的每个理想都扩展为素理想）。我们模型中的错误度量空间仅获得合理距离，并且不是超紧凑的。传递定理在Zermelo-Fraenkel环境中具有类似的独立性，回答了Good，Tree和Watson的问题。

更新日期：2020-10-19

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