On strong 𝑃-points

Blass, Andreas; Hrušák, Michael; Verner, Jonathan

doi:10.1090/S0002-9939-2013-11518-2

On strong $P$-points
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by Andreas Blass, Michael Hrušák and Jonathan Verner PDF

Proc. Amer. Math. Soc. 141 (2013), 2875-2883 Request permission

Abstract:

This paper investigates the combinatorial property of ultrafilters where the Mathias forcing relativized to them does not add dominating reals. We prove that the characterization due to Hrušák and Minami is equivalent to the strong $P$-point property. We also consistently construct a $P$-point that has no rapid Rudin-Keisler predecessor but that is not a strong $P$-point. These results answer questions of Canjar and Laflamme.

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