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The tree property and the failure of SCH at uncountable cofinality
Archive for Mathematical Logic 51 (5-6):553-562 (2012)
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+.DOI
10.1007/s00153-012-0281-z
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Citations of this work
Diagonal supercompact Radin forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.
The tree property at first and double successors of singular cardinals with an arbitrary gap.Alejandro Poveda - 2020 - Annals of Pure and Applied Logic 171 (5):102778.
The tree property at the successor of a singular limit of measurable cardinals.Mohammad Golshani - 2018 - Archive for Mathematical Logic 57 (1-2):3-25.
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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