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

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

3 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 - 1 Jul 2024
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1112/jlms.12957

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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.",

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AU - Rinot, Assaf

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AU - You, Zhixing

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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.

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DO - 10.1112/jlms.12957

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Full Souslin trees at small cardinals

Abstract

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