A long chain of P-points-Reference-Cited by-同舟云学术

A long chain of P-points

Published:2018-06 Issue:01 Volume:18 Page:1850004
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Kuzeljevic Borisa¹,Raghavan Dilip¹

Affiliation:

1. Department of Mathematics, National University of Singapore, Singapore 119076, Singapore

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 (CH) 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061318500046

Reference14 articles.

1. Tukey types of ultrafilters

2. A new class of Ramsey-classification theorems and their application in the Tukey theory of ultrafilters, Part 1

3. A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2

4. Forcing with filters and complete combinatorics

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