Chains of P-points
2019 ◽
Vol 62
(4)
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pp. 856-868
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AbstractIt 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.
2008 ◽
Vol 11
(4)
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pp. 403-413
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Keyword(s):
1984 ◽
Vol 20
(5)
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pp. 521-530
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