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

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

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
, Spencer Unger
, Dima Sinapova

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

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 _ω ₂.

Original language	English
Pages (from-to)	600-608
Number of pages	9
Journal	Transactions of the American Mathematical Society
Volume	86
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2020.11
Publication status	Published - Jun 2021

Austrian Fields of Science 2012

101013 Mathematical logic

Keywords

ARONSZAJN TREES
forcing
singular cardinal
tree property

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10.1017/jsl.2020.11

Cite this

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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 ω 2. ",

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AU - Unger, Spencer

AU - Sinapova, Dima

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KW - forcing

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KW - tree property

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

Abstract

Austrian Fields of Science 2012

Keywords

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