Aronszajn and Kurepa trees

Archive for Mathematical Logic 57 (1-2):83-90 (2018)
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Abstract

Monroe Eskew and \, 2016. https://mathoverflow.net/questions/217951/tree-properties-on-omega-1-and-omega-2) asked whether the tree property at \ implies there is no Kurepa tree. We prove that the tree property at \ is consistent with the existence of \-trees with as many branches as desired.

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10.1007/s00153-017-0579-y

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Reviewed Work: Recent papers on the tree property. Aronszajn trees and failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic, vol. 9, no. 1 , The tree property at ℵ ω+1. Journal of Symbolic Logic, vol. 77, no. 1 , The tree property and the failure of SCH at uncountable confinality. Archive for Mathematical Logic, vol. 51, no. 5-6 , The tree property and the failure of the Singular Cardinal Hypothesis at [image]. Journal of Symbolic Logic, vol. 77, no. 3 , Aronszajn trees and the successors of a singular cardinal. Archive for Mathematical Logic, vol. 52, no. 5-6 , The tree property up to ℵ ω+1. Journal of Symbolic Logic. vol. 79, no. 2 by Itay Neeman; Dima Sinapova; Spencer Unger. [REVIEW]Review by: James Cummings - 2015 - Bulletin of Symbolic Logic 21 (2):188-192.
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Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
Itay Neeman. Aronszajn trees and failure of the Singular Cardinal Hypothesis. Journal of Mathematical Logic, vol. 9, no. 1 , pp. 139–157. - Dima Sinapova. The tree property at אּω+1. Journal of Symbolic Logic, vol. 77, no. 1 , pp. 279–290. - Dima Sinapova. The tree property and the failure of SCH at uncountable cofinality. Archive for Mathematical Logic, vol. 51, no. 5-6 , pp. 553–562. - Dima Sinapova. The tree property and the failure of the Singular Cardinal Hypothesis at אּω2. Journal of Symbolic Logic, vol. 77, no. 3 , pp. 934–946. - Spencer Unger. Aronszajn trees and the successors of a singular cardinal. Archive for Mathematical Logic, vol. 52, no. 5-6 , pp. 483–496. - Itay Neeman. The tree property up to אּω+1. Journal of Symbolic Logic. vol. 79, no. 2 , pp. 429–459. [REVIEW]James Cummings - 2015 - Bulletin of Symbolic Logic 21 (2):188-192.

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Citations of this work

Easton's theorem for the tree property below ℵ.Šárka Stejskalová - 2021 - Annals of Pure and Applied Logic 172 (7):102974.

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References found in this work

Aronszajn trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
Aronszajn trees on [aleph]2 and [aleph]3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213.

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