The tree property and the failure of the Singular Cardinal Hypothesis at ℵω2

Journal of Symbolic Logic 77 (3):934-946 (2012)
  Copy   BIBTEX

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 ω²

Categories

Keywords

Reprint years

DOI

10.2178/jsl/1344862168

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 100,793

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

The tree property at ℵ ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
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.
The tree property and the failure of SCH at uncountable cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
The tree property at [image].Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279 - 290.
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.
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.
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.
On the consistency of the definable tree property on ℵ.Amir Leshem - 2000 - Journal of Symbolic Logic 65 (3):1204 - 1214.
The consistency strength of successive cardinals with the tree property.Matthew Foreman, Menachem Magidor & Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (4):1837-1847.
Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.

Analytics

Added to PP
2012-11-06

Downloads
43 (#498,107)

6 months
9 (#433,641)

Historical graph of downloads
How can I increase my downloads?

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.
Fragility and indestructibility II.Spencer Unger - 2015 - Annals of Pure and Applied Logic 166 (11):1110-1122.
Diagonal supercompact Radin forcing.Omer Ben-Neria, Chris Lambie-Hanson & Spencer Unger - 2020 - Annals of Pure and Applied Logic 171 (10):102828.

View all 7 citations / Add more citations

References found in this work

Set Theory.Keith J. Devlin - 1981 - Journal of Symbolic Logic 46 (4):876-877.
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.

Add more references