The tree property at [image]

Journal of Symbolic Logic 77 (1):279 - 290 (2012)
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Abstract

We show that given ω many supercompact cardinals, there is a generic extension in which there are no Aronszajn trees at $\aleph_{\omega + 1}$ . This is an improvement of the large cardinal assumptions. The previous hypothesis was a huge cardinal and ω many supercompact cardinals above it, in Magidor—Shelah [7]

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10.2178/jsl/1327068703

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Citations of this work

Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
A remark on the tree property in a choiceless context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.

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References found in this work

Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Scales, squares and reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
The tree property at successors of singular cardinals.Menachem Magidor & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):385-404.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.

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