A long chain of P-points

Abstract

The notion of a $\delta$-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each $\delta <{\omega }_2$, any $\delta$-generic sequence of P-points can be extended to an ${\omega }_2$-generic sequence. This shows that the Continuum Hypothesis implies that there is a chain of P-points of length ${\mathfrak{c}}^{+}$ with respect to both Rudin-Keisler and Tukey reducibility. The proofs can be easily adapted to get such a chain of length ${\mathfrak{c}}^{+}$ under a more general hypothesis like Martin's Axiom. These results answer an old question of Andreas Blass.

arXiv comment29 pages, submitted