On the consistency of the definable tree property on ℵ

Journal of Symbolic Logic 65 (3):1204 - 1214 (2000)
  Copy   BIBTEX

Abstract

In this paper we prove the equiconsistency of "Every ω 1 -tree which is first order definable over (H ω 1 ·ε) has a cofinal branch" with the existence of a Π 1 1 reflecting cardinal. We also prove that the addition of MA to the definable tree property increases the consistency strength to that of a weakly compact cardinal. Finally we comment on the generalization to higher cardinals

Categories

Keywords

Reprint years

DOI

10.2307/2586696

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

On the Consistency of the Definable Tree Property on $\aleph_1$.Amir Leshem - 2000 - Journal of Symbolic Logic 65 (3):1204-1214.
Trees and Π 1 1 -Subsets of ω1 ω 1.Alan Mekler & Jouko Vaananen - 1993 - Journal of Symbolic Logic 58 (3):1052 - 1070.
The tree property and the failure of the Singular Cardinal Hypothesis at ℵω2.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (3):934-946.
Martin's axioms, measurability and equiconsistency results.Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (1):78-94.
The tree property at א ω+2.Sy-David Friedman & Ajdin Halilović - 2011 - Journal of Symbolic Logic 76 (2):477 - 490.
The tree property at ℵ ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
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.
The complexity of the core model.William Mitchell - 1998 - Journal of Symbolic Logic 63 (4):1393-1398.
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
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
58 (#355,062)

6 months
15 (#187,676)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The relative strengths of fragments of Martin's axiom.Joan Bagaria - 2024 - Annals of Pure and Applied Logic 175 (1):103330.
2004 Summer Meeting of the Association for Symbolic Logic.Wolfram Pohlers - 2005 - Bulletin of Symbolic Logic 11 (2):249-312.

Add more citations

References found in this work

No references found.

Add more references