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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ P$-points with countably many constellations


Author: Ned I. Rosen
Journal: Trans. Amer. Math. Soc. 290 (1985), 585-596
MSC: Primary 04A20; Secondary 03E05, 03H15
MathSciNet review: 792813
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Abstract: If the continuum hypothesis $ ({\text{CH}})$ is true, then for any $ P$ point ultrafilter $ D$ (on the set of natural numbers) there exist initial segments of the Rudin-Keisler ordering, restricted to (isomorphism classes of) $ P$ points which lie above $ D$, of order type $ {\aleph _1}$. In particular, if $ D$ is an $ {\text{RK}}$-minimal ultrafilter, then we have $ ({\text{CH}})$ that there exist $ P$-points with countably many constellations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0792813-8
PII: S 0002-9947(1985)0792813-8
Article copyright: © Copyright 1985 American Mathematical Society