Aronszajn trees and the successors of a singular cardinal

Archive for Mathematical Logic 52 (5-6):483-496 (2013)
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Abstract

From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees

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10.1007/s00153-013-0326-y

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Citations of this work

Fragility and indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
A model of Cummings and Foreman revisited.Spencer Unger - 2014 - Annals of Pure and Applied Logic 165 (12):1813-1831.
The eightfold way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.
The tree property at and.Dima Sinapova & Spencer Unger - 2018 - Journal of Symbolic Logic 83 (2):669-682.

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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 on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.

View all 9 references / Add more references