P-Filters and the perfect set property

Jialiang He; Shuguo Zhang

doi:10.1016/j.topol.2013.11.006

P-Filters and the perfect set property

Jialiang He, Shuguo Zhang

Sichuan University

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

Abstract

In this paper, we prove that every non-meager P-filter F is a PSP(σ11)-filter (that is, A∩F has the perfect set property whenever A is an analytic subset of 2^•) and the filter product of a Ramsey ultrafilter and a P•2-point is a PSP(σ11)-ultrafilter. These theorems strengthen a result of Miller and answer some questions asked by Andrea Medini and David Milovich.

Original language	English
Pages (from-to)	12-19
Number of pages	8
Journal	Topology and its Applications
Volume	162
Issue number	1
DOIs	https://doi.org/10.1016/j.topol.2013.11.006
State	Published - 1 Feb 2014
Externally published	Yes

Bibliographical note

Funding Information:
This work was supported by NSFC Grants # 10971149 and # 11271272 .

Funding

This work was supported by NSFC Grants # 10971149 and # 11271272 .

Funders	Funder number
National Natural Science Foundation of China	10971149, 11271272

Keywords

Non-meager P-filter
P-point
PSP(σ11)-ultrafilter
P•2-point
Ramsey ultrafilter

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10.1016/j.topol.2013.11.006

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author = "Jialiang He and Shuguo Zhang",

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PY - 2014/2/1

Y1 - 2014/2/1

N2 - In this paper, we prove that every non-meager P-filter F is a PSP(σ11)-filter (that is, A∩F has the perfect set property whenever A is an analytic subset of 2•) and the filter product of a Ramsey ultrafilter and a P•2-point is a PSP(σ11)-ultrafilter. These theorems strengthen a result of Miller and answer some questions asked by Andrea Medini and David Milovich.

AB - In this paper, we prove that every non-meager P-filter F is a PSP(σ11)-filter (that is, A∩F has the perfect set property whenever A is an analytic subset of 2•) and the filter product of a Ramsey ultrafilter and a P•2-point is a PSP(σ11)-ultrafilter. These theorems strengthen a result of Miller and answer some questions asked by Andrea Medini and David Milovich.

KW - Non-meager P-filter

KW - P-point

KW - PSP(σ11)-ultrafilter

KW - P•2-point

KW - Ramsey ultrafilter

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JO - Topology and its Applications

JF - Topology and its Applications

IS - 1

ER -

P-Filters and the perfect set property

Abstract

Bibliographical note

Funding

Keywords

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