Geodesic
Chains of P-points
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 856-868

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DOI

It is proved that the Continuum Hypothesis implies that any sequence of rapid P-points of length ${<}\mathfrak{c}^{+}$ that is increasing with respect to the Rudin–Keisler ordering is bounded above by a rapid P-point. This is an improvement of a result from B. Kuzeljevic and D. Raghavan. It is also proved that Jensen’s diamond principle implies the existence of an unbounded strictly increasing sequence of P-points of length $\unicode[STIX]{x1D714}_{1}$ in the Rudin–Keisler ordering. This shows that restricting to the class of rapid P-points is essential for the first result.
DOI : 10.4153/S0008439519000043
Mots-clés : Rudin–Keisler order, ultrafilter, P-point 
Raghavan, Dilip; Verner, Jonathan L. Chains of P-points. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 856-868. doi: 10.4153/S0008439519000043
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     title = {Chains of {P-points}},
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     year = {2019},
     volume = {62},
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     doi = {10.4153/S0008439519000043},
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