THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL

James Cummings; Yair Hayut; Menachem Magidor; Itay Neeman; Dima Sinapova; Spencer Unger

doi:10.1017/jsl.2020.11

THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL

James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova, Spencer Unger

Einstein Institute of Mathematics

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

Abstract

We present an alternative proof that from large cardinals, we can force the tree property at κ⁺ and κ⁺⁺ simultaneously for a singular strong limit cardinal κ. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for κ = ℵ_ω₂.

Original language	English
Pages (from-to)	600-608
Number of pages	9
Journal	Journal of Symbolic Logic
Volume	86
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2020.11
State	Published - 1 Jun 2021

Bibliographical note

Publisher Copyright:
© 2020, Association for Symbolic Logic

Keywords

forcing
singular cardinal
tree property

Access to Document

10.1017/jsl.2020.11

Cite this

@article{7608a09dacb84ab7a946fe66bc0d44df,

title = "THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL",

abstract = "We present an alternative proof that from large cardinals, we can force the tree property at κ+ and κ++ simultaneously for a singular strong limit cardinal κ. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for κ = ℵω2.",

keywords = "forcing, singular cardinal, tree property",

author = "James Cummings and Yair Hayut and Menachem Magidor and Itay Neeman and Dima Sinapova and Spencer Unger",

note = "Publisher Copyright: {\textcopyright} 2020, Association for Symbolic Logic",

year = "2021",

month = jun,

day = "1",

doi = "10.1017/jsl.2020.11",

language = "אנגלית",

volume = "86",

pages = "600--608",

journal = "Journal of Symbolic Logic",

issn = "0022-4812",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL

AU - Cummings, James

AU - Hayut, Yair

AU - Magidor, Menachem

AU - Neeman, Itay

AU - Sinapova, Dima

AU - Unger, Spencer

PY - 2021/6/1

Y1 - 2021/6/1

N2 - We present an alternative proof that from large cardinals, we can force the tree property at κ+ and κ++ simultaneously for a singular strong limit cardinal κ. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for κ = ℵω2.

AB - We present an alternative proof that from large cardinals, we can force the tree property at κ+ and κ++ simultaneously for a singular strong limit cardinal κ. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for κ = ℵω2.

KW - forcing

KW - singular cardinal

KW - tree property

UR - http://www.scopus.com/inward/record.url?scp=85129505789&partnerID=8YFLogxK

U2 - 10.1017/jsl.2020.11

DO - 10.1017/jsl.2020.11

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85129505789

SN - 0022-4812

VL - 86

SP - 600

EP - 608

JO - Journal of Symbolic Logic

JF - Journal of Symbolic Logic

IS - 2

ER -

THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this