Nice ℵ1 generated non‐P‐points, Part I

We define a family of non‐principal ultrafilters on N${\mathbb {N}}$ which are, in a sense, very far from P‐points. We prove the existence of such ultrafilters under reasonable conditions. In subsequent articles, we intend to prove that such ultrafilters may exist while no P‐point exists. Though our...

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Bibliographic Details
Published in:Mathematical logic quarterly 2023-02, Vol.69 (1), p.117-129
Main Author: Shelah, Saharon
Format: Article
Language:English
Subjects:
Combinatorial analysis
Online Access:Get full text
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Summary:We define a family of non‐principal ultrafilters on N${\mathbb {N}}$ which are, in a sense, very far from P‐points. We prove the existence of such ultrafilters under reasonable conditions. In subsequent articles, we intend to prove that such ultrafilters may exist while no P‐point exists. Though our primary motivations came from forcing and independence results, the family of ultrafilters introduced here should be interesting from combinatorial point of view too.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202200070