On the equivalence of Rudin's Lemma and the Boolean prime ideal theorem
On the equivalence of Rudin's Lemma and the Boolean prime ideal theorem
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DOI：
10.1016/j.topol.2021.107970
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Qingguo Li
中科院分区：
文献类型：
--
作者：
Mengqiao Huang;Xiaodong Jia;Qingguo Li
Rudin's Lemma, which appeared more than forty years ago, is a consequence of the Axiom of Choice and has been playing fundamental roles in the study of quasicontinuity in domain theory. This note aims to revealing the fact that Rudin's Lemma (and its variants) and the Boolean prime ideal theorem are equivalent in Zermelo-Fraenkel Set Theory, which is choiceless Set Theory. Our main techniques rely on Erné's Separation Lemma for Locales and a variant of Rado's Selection Principle due to Cowen.
