2012/04/18 by Andrzej Starosolski, Starosolski, Andrzej
Mathematics · #03E05 #03E17 #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Mathematical Dynamics and Fractals #math.LO #msc:03E05 #msc:03E17
paper · pdf · doi:10.48550/arxiv.1204.4173
11 pages
arxiv created 2012/04/18 · openalex publication_date 2012/04/18 · arxiv updated 2012/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
M. E. Rudin in "Partial orders on the types of βN", (Trans. Amer. Math. Soc., 155, 1971, 353-362) proved (under CH) that for each P-point u there is a P-point v such that v>RKu. A. Blass in "Rudin - Kisler ordering on P-points" (Trans. Amer. Math. Soc. 179, 1973, 145-166) improved that theorem assuming MA in the place of CH, in that paper he also proved that under MA each RK-increasing sequence of P-points is upper bounded by a P-point. We improve Blass results simultaneously in 3 directions - we prove it for each class of index ≥ 2 of P-hierarchy (P-points coincidence with a class P2 of P-hierarchy), assuming \mathfrakb=\mathfrakc in the place of MA and we show that there are at least \mathfrakb many Rudin-Kisler incomparable such upper bounds.