2018/03/10 by Andrzej Starosolski, Starosolski, Andrzej
Mathematics · #Advanced Topology and Set Theory #Limits and Structures in Graph Theory #Advanced Banach Space Theory
paper · pdf · doi:10.48550/arxiv.1803.03862
M. E. Rudin proved under CH that for each P-point there exists another P-point strictly RK-greater (M. E. Rudin, Partial orders on the types of βℕ , Trans. Amer. Math. Soc., 155 (1971), 353-362). Assuming \mathfrakp=\mathfrakc A. Blass showed the same, and proved that each RK-increasing ω-sequence of P-points is upper bounded by a P-point, and that there is an order embedding of the real line into the class of P-points with respect to the RK-(pre)ordering (A. Blass, Rudin - Keisler ordering on P-points, Trans. Amer. Math. Soc., 179 (1973), 145-166). In the present paper the results cited above are proved under a (weaker) assumption \mathfrakb=\mathfrakc. A. Blass also asked in (A. Blass, Rudin - Keisler ordering on P-points, Trans. Amer. Math. Soc., 179 (1973), 145-166) what ordinals can be embedded in the set of P-points and pointed out, that such an ordinal may not be greater then \mathfrakc+. In the present paper the question is answered showing (under \mathfrakb = \mathfrakc) that there is an order embedding of \mathfrakc+ into P-points.