Gruff ultrafilterd and the ideal of scattered set

Abstract:

We study gruff ultrafilters on the rational numbers and give some constructions under CH with some additional properties. We also compare gruff ultrafilters and P-points. To do this, it will be necessary to study the ideal of scattered sets of Q. .

Keywords: Gruff Ultrafilter||Scattered||Crowded||Rational numbers

MSC: 03E05 (54G12 54H05)

Journal: Topology and its Applications

ISSN: 1879-3207

Year: 2026

Volume: 382

Pages: 109761

MR Number: 5039606

Revision: 1

URL: https://www.sciencedirect.com/science/article/pii/S0166864126000519?via%3Dihub

DOI: 10.1016/j.topol.2026.109761