There may be simple Pℵ1 and Pℵ2-points and the Rudin-Keisler ordering may be downward directed

Annals of Pure and Applied Logic 33 (C):213-243 (1987)
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Citations of this work

Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.
Special ultrafilters and cofinal subsets of $$({}^omega omega, <^*)$$.Peter Nyikos - 2020 - Archive for Mathematical Logic 59 (7-8):1009-1026.
Ramsey ultrafilters and the reaping number—con(r.M. Goldstern & S. Shelah - 1990 - Annals of Pure and Applied Logic 49 (2):121-142.

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Proper Forcing.Saharon Shelah - 1985 - Journal of Symbolic Logic 50 (1):237-239.

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