Generic existence of interval P-points

Jialiang He; Renling Jin; Shuguo Zhang

doi:10.1007/s00153-022-00853-3

Generic existence of interval P-points

Jialiang He, Renling Jin, Shuguo Zhang

Research output: Contribution to journal › Article › peer-review

Abstract

A P-point ultrafilter over ω is called an interval P-point if for every function from ω to ω there exists a set A in this ultrafilter such that the restriction of the function to A is either a constant function or an interval-to-one function. In this paper we prove the following results. (1) Interval P-points are not isomorphism invariant under CH or MA. (2) We identify a cardinal invariant non^{∗ ∗}(I_int) such that every filter base of size less than continuum can be extended to an interval P-point if and only if non^{∗ ∗}(I_int) = c. (3) We prove the generic existence of slow/rapid non-interval P-points and slow/rapid interval P-points which are neither quasi-selective nor weakly Ramsey under the assumption d= c or cov(B) = c.

Original language	English
Pages (from-to)	619-640
Number of pages	22
Journal	Archive for Mathematical Logic
Volume	62
Issue number	5-6
DOIs	https://doi.org/10.1007/s00153-022-00853-3
State	Published - Jul 2023
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

Jialiang He: Supported in part by a National Science Foundation of China Grant #11801386. Renling Jin: Supported in part by a collaboration research Grant #513023 from Simons Foundation. Shuguo Zhang: Supported in part by a National Science Foundation of China Grant #11771311.

Funders	Funder number
Simons Foundation
National Natural Science Foundation of China	11771311, 513023, 1180010236, 11801386

Keywords

Generic existence
Interval P-point
P-point
Quasi-selective ultrafilter
Weakly Ramsey ultrafilter

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10.1007/s00153-022-00853-3

Cite this

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Generic existence of interval P-points

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Keywords

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