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

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Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.
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On Some Small Cardinals for Boolean Algebras.Ralph Mckenzie & J. Donald Monk - 2004 - Journal of Symbolic Logic 69 (3):674-682.

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