On the consistency of the definable tree property on א1

Amir Leshem

doi:10.2307/2586696

On the consistency of the definable tree property on א₁

Amir Leshem^*

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper we prove the equiconsistency of "Every ω₁ - tree which is first order definable over (H_ω1 , ε) has a cofinal branch" with the existence of a Π¹₁ 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.

Original language	English
Pages (from-to)	1204-1214
Number of pages	11
Journal	Journal of Symbolic Logic
Volume	65
Issue number	3
DOIs	https://doi.org/10.2307/2586696
State	Published - Sep 2000

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On the consistency of the definable tree property on א₁

Abstract

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