A long chain of P-points

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Journal of Mathematical Logic 18 (1):1850004 (2018)
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Abstract

The notion of a [Formula: see text]-generic sequence of P-points is introduced in this paper. It is proved assuming the Continuum Hypothesis that for each [Formula: see text], any [Formula: see text]-generic sequence of P-points can be extended to an [Formula: see text]-generic sequence. This shows that the CH implies that there is a chain of P-points of length [Formula: see text] with respect to both Rudin–Keisler and Tukey reducibility. These results answer an old question of Andreas Blass.

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10.1142/s0219061318500046

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Citations of this work

Cofinal types on ω 2.Borisa Kuzeljevic & Stevo Todorcevic - 2023 - Mathematical Logic Quarterly 69 (1):92-103.
Lower Bounds of Sets of P-points.Borisa Kuzeljevic, Dilip Raghavan & Jonathan L. Verner - 2023 - Notre Dame Journal of Formal Logic 64 (3):317-327.
The rudin–keisler ordering of p-points under ???? = ????Andrzej Starosolski - 2021 - Journal of Symbolic Logic 86 (4):1691-1705.

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References found in this work

Forcing with filters and complete combinatorics.Claude Laflamme - 1989 - Annals of Pure and Applied Logic 42 (2):125-163.
Cofinal types of ultrafilters.Dilip Raghavan & Stevo Todorcevic - 2012 - Annals of Pure and Applied Logic 163 (3):185-199.
The Rudin-Blass ordering of ultrafilters.Claude Laflamme & Jian-Ping Zhu - 1998 - Journal of Symbolic Logic 63 (2):584-592.

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