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