On the ideal J[κ]

Assaf Rinot

doi:10.1016/j.apal.2021.103055

On the ideal J[κ]

Assaf Rinot

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

6 Scopus citations

Abstract

Motivated by a question from a recent paper by Gilton, Levine and Stejskalová, we obtain a new characterization of the ideal J[κ], from which we confirm that κ-Souslin trees exist in various models of interest. As a corollary we get that for every integer n such that b<2^ℵ_n=ℵ_n+1, if □(ℵ_n+1) holds, then there exists an ℵ_n+1-Souslin tree.

Original language	English
Article number	103055
Journal	Annals of Pure and Applied Logic
Volume	173
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2021.103055
State	Published - 1 Feb 2022
Externally published	Yes

Keywords

Souslin tree
square
xbox

ASJC Scopus subject areas

Logic

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10.1016/j.apal.2021.103055

Cite this

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title = "On the ideal J[κ]",

abstract = "Motivated by a question from a recent paper by Gilton, Levine and Stejskalov{\'a}, we obtain a new characterization of the ideal J[κ], from which we confirm that κ-Souslin trees exist in various models of interest. As a corollary we get that for every integer n such that b<2ℵn=ℵn+1, if □(ℵn+1) holds, then there exists an ℵn+1-Souslin tree.",

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N2 - Motivated by a question from a recent paper by Gilton, Levine and Stejskalová, we obtain a new characterization of the ideal J[κ], from which we confirm that κ-Souslin trees exist in various models of interest. As a corollary we get that for every integer n such that b<2ℵn=ℵn+1, if □(ℵn+1) holds, then there exists an ℵn+1-Souslin tree.

AB - Motivated by a question from a recent paper by Gilton, Levine and Stejskalová, we obtain a new characterization of the ideal J[κ], from which we confirm that κ-Souslin trees exist in various models of interest. As a corollary we get that for every integer n such that b<2ℵn=ℵn+1, if □(ℵn+1) holds, then there exists an ℵn+1-Souslin tree.

KW - Souslin tree

KW - square

KW - xbox

UR - https://www.scopus.com/pages/publications/85116796127

U2 - 10.1016/j.apal.2021.103055

DO - 10.1016/j.apal.2021.103055

M3 - Article

AN - SCOPUS:85116796127

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ER -

On the ideal J[κ]

Abstract

Keywords

ASJC Scopus subject areas

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