The strong tree property and the failure of SCH

Archive for Mathematical Logic 58 (7-8):867-875 (2019)
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Abstract

Fontanella :193–207, 2014) showed that if \ is an increasing sequence of supercompacts and \, then the strong tree property holds at \. Building on a proof by Neeman, we show that the strong tree property at \ is consistent with \, where \ is singular strong limit of countable cofinality.

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10.1007/s00153-019-00663-0

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Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
The tree property up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
A model of Cummings and Foreman revisited.Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (12):1813-1831.
Strong tree properties for small cardinals.Laura Fontanella - 2013 - Journal of Symbolic Logic 78 (1):317-333.
The tree property at and.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.

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