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On the Consistency of the Definable Tree Property on $\aleph_1$
Journal of Symbolic Logic 65 (3):1204-1214 (2000)
Abstract
In this paper we prove the equiconsistency of "Every $\omega_1$-tree which is first order definable over has a cofinal branch" with the existence of a $\Pi^1_1$ 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.My notes
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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.
References found in this work
Aronszajn trees and the independence of the transfer property.William Mitchell - 1972 - Annals of Mathematical Logic 5 (1):21.
Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
Aronszajn trees on [aleph]2 and [aleph]3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213.
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