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On the consistency of the Definable Tree Property on ℵ1

  • Amir Leshem (a1) (a2)

Abstract

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

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