Paper detail

A long chain of P-points

The notion of a $δ$-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each $δ< ω_{2}$, any $δ$-generic sequence of P-points can be extended to an $ω_{2}$-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.