The consistency strength of successive cardinals with the tree property

, &
Journal of Symbolic Logic 66 (4):1837-1847 (2001)
  Copy   BIBTEX

Abstract

If ω n has the tree property for all $2 \leq n and $2^{ , then for all X ∈ H ℵ ω and $n exists

Categories

Keywords

Reprint years

DOI

10.2307/2694979

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 106,716

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 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 א ω+2.Sy-David Friedman & Ajdin Halilović - 2011 - Journal of Symbolic Logic 76 (2):477 - 490.
On the consistency of the definable tree property on ℵ.Amir Leshem - 2000 - Journal of Symbolic Logic 65 (3):1204 - 1214.
The tree property and the failure of the Singular Cardinal Hypothesis at ℵω2.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (3):934-946.
The tree property at ℵ ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
The consistency strength of long projective determinacy.Juan P. Aguilera & Sandra Müller - 2019 - Journal of Symbolic Logic 85 (1):338-366.
The Strong and Super Tree Properties at Successors of Singular Cardinals.William Adkisson - 2024 - Journal of Symbolic Logic 89 (3):1251-1283.
Free subsets in internally approachable models.P. D. Welch - 2025 - Archive for Mathematical Logic 64 (3):435-443.
The tree property below ℵ ω ⋅ 2.Spencer Unger - 2016 - Annals of Pure and Applied Logic 167 (3):247-261.
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.

Analytics

Added to PP
2009-01-28

Downloads
73 (#313,585)

6 months
8 (#533,264)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The tree property up to אω+1.Itay Neeman - 2014 - Journal of Symbolic Logic 79 (2):429-459.
The tree property and the continuum function below.Radek Honzik & Šárka Stejskalová - 2018 - Mathematical Logic Quarterly 64 (1-2):89-102.
A remark on the tree property in a choiceless context.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (5-6):585-590.
Easton's theorem for the tree property below ℵ.Šárka Stejskalová - 2021 - Annals of Pure and Applied Logic 172 (7):102974.

Add more citations

References found in this work

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.
Projectively well-ordered inner models.J. R. Steel - 1995 - Annals of Pure and Applied Logic 74 (1):77-104.
Optimal proofs of determinacy.Itay Neeman - 1995 - Bulletin of Symbolic Logic 1 (3):327-339.

View all 7 references / Add more references