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),were solve open problems from Keremedis, Olfati and Wajch "OnP-spaces and G delta-sets in the absence of the Axiom of Choice" on the deductive strength of statements concerning P-spaces and strongly quasi Bairespaces via positive and independence results. For some of the independence results, we construct three new per mutation models of ZFA+<not sign>AC,where ZFA denotes the ZermeloFraenkel set theory with atoms. Part of our ZFA-independence proofs are transferable to ZF(i.e. Zermelo-Fraenkel set theory without AC)