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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)
Keywords:
ultrafilter; $$P$$-point; $$P$$-ideal
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