On strong \(P\)-points
\textit{M. Canjar} [Ann. Pure Appl. Logic 37, No. 1, 1--79 (1988; Zbl 0646.03025)] first investigated the question: When does the Mathias forcing relativized to an ultrafilter on \(\omega\) add no dominating reals (it is called \textit{Canjar ultrafilter} in this paper)? Later, \textit{C. Laflamme} [Ann. Pure Appl. Logic 42, No. 2, 125--163 (1989; Zbl 0681.03035)] introduced the notion of a \textit{strong \(P\)-point} and noted it as a necessary condition for a Canjar ultrafilter. \textit{M. Hrušák} and \textit{H. Minami} recently introduced [Ann. Pure Appl. Logic 165, No. 3, 880--894 (2014; Zbl 1306.03023)] an equivalent combinatorial condition for being a Canjar ultrafilter. Via this characterization, the authors show in this paper that an ultrafilter on \(\omega\) is a Canjar ultrafilter iff it is a strong \(P\)-point.NEWLINENEWLINECanjar showed in [loc. cit.] that a Canjar ultrafilter must be a \(P\)-point with no rapid Rudin-Keisler predecessor. In Section 3 of this paper, under the hypothesis that cov\(({\mathcal M})={\mathfrak c}\), the authors construct a \(P\)-point which is not strong, and neither has a rapid Rudin-Keisler predecessor.
scientific article; zbMATH DE number 6184487