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On the consistency of the Definable Tree Property on ℵ1

Published online by Cambridge University Press:  12 March 2014

Amir Leshem
Amir Leshem*
Affiliation:
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel E-mail: leshem@math.huji.ac.il Circuit and Systems Group, Faculty of Information Technology and Systems, Delft University of Technology, Mekelweg 4, 2628CD Delft, the Netherlands E-mail: leshem@cas.et.tudelft.nl
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 1204 - 1214
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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