The tree property and the failure of SCH at uncountable cofinality

Archive for Mathematical Logic 51 (5-6):553-562 (2012)
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Abstract

Given a regular cardinal λ and λ many supercompact cardinals, we describe a type of forcing such that in the generic extension there is a cardinal κ with cofinality λ, the Singular Cardinal Hypothesis at κ fails, and the tree property holds at κ+.

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References found in this work

Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
The tree property at successors of singular cardinals.Menachem Magidor & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):385-404.
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
Diagonal Prikry extensions.James Cummings & Matthew Foreman - 2010 - Journal of Symbolic Logic 75 (4):1383-1402.
A model for a very good scale and a bad scale.Dima Sinapova - 2008 - Journal of Symbolic Logic 73 (4):1361-1372.

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