Aronszajn trees on ℵ2 and ℵ3

Annals of Mathematical Logic 24 (3):213-230 (1983)
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Abstract

Assuming the existence of a supercompact cardinal and a weakly compact cardinal above it, we provide a generic extension where there are no Aronszajn trees of height ω 2 or ω 3 . On the other hand we show that some large cardinal assumptions are necessary for such a consistency result

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10.1016/0168-0072(83)90006-4

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Citations of this work

The tree property up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
Fragility and indestructibility of the tree property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
The Eightfold Way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.

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Proper Forcing.Saharon Shelah - 1985 - Journal of Symbolic Logic 50 (1):237-239.

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