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

Annals of Pure and Applied Logic 33 (3):213-243 (1987)
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DOI 10.1016/0168-0072(87)90082-0
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References found in this work BETA

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

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Citations of this work BETA

Q-Pointness, P-Pointness and Feebleness of Ideals.Pierre Matet & Janusz Pawlikowski - 2003 - Journal of Symbolic Logic 68 (1):235-261.
Continuum Cardinals Generalized to Boolean Algebras.J. Donald Monk - 2001 - Journal of Symbolic Logic 66 (4):1928-1958.
On Some Small Cardinals for Boolean Algebras.Ralph McKenzie & J. Donald Monk - 2004 - Journal of Symbolic Logic 69 (3):674-682.
The Rudin-Blass Ordering of Ultrafilters.Claude Laflamme & Jian-Ping Zhu - 1998 - Journal of Symbolic Logic 63 (2):584-592.

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