A note on \(\mathcal{J}\)-ultrafilters and \(P\)-points. (English) Zbl 1163.03027

Flašková, Jana

Acta Univ. Carol., Math. Phys. 48, No. 2, 43-48 (2007).

Summary: We consider the question whether \(P\)-points can be characterized as \(\mathcal J\)-ultrafilters for \(\mathcal J\) an ideal on \(\omega\) and show that (consistently) it is not possible if \(\mathcal J\) is an \(F_\sigma\)-ideal or a \(P\)-ideal.

MSC:

03E05	Other combinatorial set theory
03E35	Consistency and independence results
54H05	Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)

Keywords:

ultrafilter; \(P\)-point; \(P\)-ideal