On the relationship between mutual and tight stationarity

William Chen-Mertens; Itay Neeman

doi:10.1016/j.apal.2021.102963

On the relationship between mutual and tight stationarity

William Chen-Mertens, Itay Neeman

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

Abstract

We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω₁ ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.

Original language	English
Article number	102963
Journal	Annals of Pure and Applied Logic
Volume	172
Issue number	7
DOIs	https://doi.org/10.1016/j.apal.2021.102963
State	Published - 1 Jul 2021
Externally published	Yes

Keywords

Mutual stationarity
Prikry type forcing
Singular cardinals

ASJC Scopus subject areas

Logic

Access to Document

10.1016/j.apal.2021.102963

Cite this

@article{88efdafcb3db43d5845449da7416d7f0,

title = "On the relationship between mutual and tight stationarity",

abstract = "We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω1 ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.",

keywords = "Mutual stationarity, Prikry type forcing, Singular cardinals",

author = "William Chen-Mertens and Itay Neeman",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = jul,

day = "1",

doi = "10.1016/j.apal.2021.102963",

language = "English",

volume = "172",

journal = "Annals of Pure and Applied Logic ",

issn = "0168-0072",

publisher = "Elsevier B.V.",

number = "7",

}

TY - JOUR

T1 - On the relationship between mutual and tight stationarity

AU - Chen-Mertens, William

AU - Neeman, Itay

PY - 2021/7/1

Y1 - 2021/7/1

N2 - We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω1 ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.

AB - We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary subsets consisting of cofinality ω1 ordinals, and show that such stationary sequences are mutually stationary in the presence of interleaved supercompact cardinals.

KW - Mutual stationarity

KW - Prikry type forcing

KW - Singular cardinals

UR - http://www.scopus.com/inward/record.url?scp=85102581254&partnerID=8YFLogxK

U2 - 10.1016/j.apal.2021.102963

DO - 10.1016/j.apal.2021.102963

M3 - Article

AN - SCOPUS:85102581254

SN - 0168-0072

VL - 172

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 7

M1 - 102963

ER -

On the relationship between mutual and tight stationarity

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this