The tree property at the double successor of a singular cardinal with a larger gap

Sy-David Friedman; Radek Honzík; Sarka Stejskalova

doi:10.1016/j.apal.2018.02.002

The tree property at the double successor of a singular cardinal with a larger gap

Sy-David Friedman
, Radek Honzík
, Sarka Stejskalova

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, 2 ^κ=κ ⁺³=λ ⁺, and the tree property holds at κ ⁺⁺=λ. Next we generalize this result to an arbitrary cardinal μ such that κ<cf(μ) and λ ⁺≤μ. This result provides more information about possible relationships between the tree property and the continuum function.

Original language	English
Pages (from-to)	548-564
Number of pages	17
Journal	Annals of Pure and Applied Logic
Volume	169
Issue number	6
DOIs	https://doi.org/10.1016/j.apal.2018.02.002
Publication status	Published - Jun 2018

Austrian Fields of Science 2012

101013 Mathematical logic

Keywords

ARONSZAJN TREES
Singular cardinals
The tree property

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10.1016/j.apal.2018.02.002

Cite this

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abstract = "Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, 2 κ=κ +3=λ +, and the tree property holds at κ ++=λ. Next we generalize this result to an arbitrary cardinal μ such that κ+≤μ. This result provides more information about possible relationships between the tree property and the continuum function. ",

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AU - Honzík, Radek

AU - Stejskalova, Sarka

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Y1 - 2018/6

N2 - Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, 2 κ=κ +3=λ +, and the tree property holds at κ ++=λ. Next we generalize this result to an arbitrary cardinal μ such that κ+≤μ. This result provides more information about possible relationships between the tree property and the continuum function.

AB - Starting from a Laver-indestructible supercompact κ and a weakly compact λ above κ, we show there is a forcing extension where κ is a strong limit singular cardinal with cofinality ω, 2 κ=κ +3=λ +, and the tree property holds at κ ++=λ. Next we generalize this result to an arbitrary cardinal μ such that κ+≤μ. This result provides more information about possible relationships between the tree property and the continuum function.

KW - ARONSZAJN TREES

KW - Singular cardinals

KW - The tree property

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JF - Annals of Pure and Applied Logic

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ER -

The tree property at the double successor of a singular cardinal with a larger gap

Abstract

Austrian Fields of Science 2012

Keywords

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