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The tree property and the failure of the Singular Cardinal Hypothesis at ℵω2
Journal of Symbolic Logic 77 (3):934-946 (2012)
Abstract
We show that given ù many supercompact cardinals, there is a generic extension in which the tree property holds at ℵ ω²+1 and the SCH fails at ℵ ω²Links
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Citations of this work
Forcing with Sequences of Models of Two Types.Itay Neeman - 2014 - Notre Dame Journal of Formal Logic 55 (2):265-298.
Stationary Reflection and the Failure of the Sch.Omer Ben-Neria, Yair Hayut & Spencer Unger - 2024 - Journal of Symbolic Logic 89 (1):1-26.
Fragility and indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
The tree property at the ℵ 2 n 's and the failure of SCH at ℵ ω.Sy-David Friedman & Radek Honzik - 2015 - Annals of Pure and Applied Logic 166 (4):526-552.
Diagonal supercompact Radin forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.
References found in this work
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.
Canonical structure in the universe of set theory: part one.James Cummings, Matthew Foreman & Menachem Magidor - 2004 - Annals of Pure and Applied Logic 129 (1-3):211-243.
Canonical structure in the universe of set theory: Part two.James Cummings, Matthew Foreman & Menachem Magidor - 2006 - Annals of Pure and Applied Logic 142 (1):55-75.
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