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The relation of rapid ultrafilters and \(Q\)-points to van der Waerden ideal. (English) Zbl 1244.03123

Summary: We point out one of the differences between rapid ultrafilters and \(Q\)-points: rapid ultrafilters may have empty intersection with the van der Waerden ideal, whereas every \(Q\)-point has a non-empty intersection with the van der Waerden ideal. Assuming Martin’s axiom for countable posets we also construct a \({\mathcal W}\)-ultrafilter which is not a \(Q\)-point.

MSC:

03E05 Other combinatorial set theory
03E75 Applications of set theory
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