2012/01/09 by Michał Machura, Machura, Michał, Andrzej Starosolski +1
Mathematics · #03E05 #03E50 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1201.1725
openalex publication_date 2012/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Under MA we prove that for the ideal \cal I of thin sets on ω and for any ordinal γ≤ ω1 there is an \cal I-ultrafilter (in the sense of Baumgartner), which belongs to the class \cal Pγ of P-hierarchy of ultrafilters. Since the class of \cal P2 ultrafilters coincides with a class of P-points, out result generalize theorem of Flašková, which states that there are \cal I-ultrafilters which are not P-points. It is also related to theorem which states that under CH for any tall P-ideal \cal I on ω there is an \cal I-ultrafilter, however the ideal of thin sets is not P-ideal.