Full Souslin trees at small cardinals

Assaf Rinot; Shira Yadai; Zhixing You

doi:10.1112/jlms.12957

Full Souslin trees at small cardinals

Assaf Rinot, Shira Yadai, Zhixing You

Department of Mathematics

Bar-Ilan University

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

1 Scopus citations

Abstract

A (Formula presented.) -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full (Formula presented.) -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal (Formula presented.). Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be (Formula presented.) many full (Formula presented.) -trees such that the product of any countably many of them is an (Formula presented.) -Souslin tree.

Original language	English
Article number	e12957
Journal	Journal of the London Mathematical Society
Volume	110
Issue number	1
DOIs	https://doi.org/10.1112/jlms.12957
State	Published - Jul 2024

Bibliographical note

Publisher Copyright:
Journal of the London Mathematical Society© 2024 The Author(s). The Journal of the London Mathematical Society is copyright © London Mathematical Society.

Access to Document

10.1112/jlms.12957

Cite this

@article{26b2a1ee3d144ff9a44448c59ade802b,

title = "Full Souslin trees at small cardinals",

abstract = "A (Formula presented.) -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full (Formula presented.) -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal (Formula presented.). Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be (Formula presented.) many full (Formula presented.) -trees such that the product of any countably many of them is an (Formula presented.) -Souslin tree.",

author = "Assaf Rinot and Shira Yadai and Zhixing You",

note = "Publisher Copyright: Journal of the London Mathematical Society{\textcopyright} 2024 The Author(s). The Journal of the London Mathematical Society is copyright {\textcopyright} London Mathematical Society.",

year = "2024",

month = jul,

doi = "10.1112/jlms.12957",

language = "אנגלית",

volume = "110",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "John Wiley and Sons Ltd",

number = "1",

}

TY - JOUR

T1 - Full Souslin trees at small cardinals

AU - Rinot, Assaf

AU - Yadai, Shira

AU - You, Zhixing

PY - 2024/7

Y1 - 2024/7

N2 - A (Formula presented.) -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full (Formula presented.) -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal (Formula presented.). Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be (Formula presented.) many full (Formula presented.) -trees such that the product of any countably many of them is an (Formula presented.) -Souslin tree.

AB - A (Formula presented.) -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full (Formula presented.) -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal (Formula presented.). Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be (Formula presented.) many full (Formula presented.) -trees such that the product of any countably many of them is an (Formula presented.) -Souslin tree.

UR - http://www.scopus.com/inward/record.url?scp=85197390924&partnerID=8YFLogxK

U2 - 10.1112/jlms.12957

DO - 10.1112/jlms.12957

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

AN - SCOPUS:85197390924

SN - 0024-6107

VL - 110

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 1

M1 - e12957

ER -

Full Souslin trees at small cardinals

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this