On Some Open Problems about P-Spaces, Strongly Quasi Baire Spaces and Choice

In set theory without the full power of the axiom of choice ( AC ), we resolve open problems from Keremedis, Olfati and Wajch “On P -spaces and G δ -sets in the absence of the Axiom of Choice” on the deductive strength of statements concerning P -spaces and strongly quasi Baire spaces via positive a...

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Bibliographic Details
Published in:Resultate der Mathematik 2024-02, Vol.79 (1), Article 19
Main Author: Tachtsis, Eleftherios
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In set theory without the full power of the axiom of choice ( AC ), we resolve open problems from Keremedis, Olfati and Wajch “On P -spaces and G δ -sets in the absence of the Axiom of Choice” on the deductive strength of statements concerning P -spaces and strongly quasi Baire spaces via positive and independence results. For some of the independence results, we construct three new permutation models of ZFA + ¬ AC , where ZFA denotes the Zermelo–Fraenkel set theory with atoms. Part of our ZFA -independence proofs are transferable to ZF (i.e. Zermelo–Fraenkel set theory without AC ).
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-02049-4