On the consistency of the definable tree property on \aleph_1
Logic
2007-05-23 v1 Combinatorics
Abstract
In this paper we prove the equiconsistency of ``Every omega_1 tree which is first order definable over H_{omega_1} has a cofinal branch'' with the existence of a Pi^1_1 reflecting cardinal. The proof uses a definable version of Ramsey theorem on aleph_1 which is again equiconsistent with a Pi^1_1 reflecting cardinal. We also prove that the addition of 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.
Keywords
Cite
@article{arxiv.math/0005208,
title = {On the consistency of the definable tree property on \aleph_1},
author = {Amir Leshem},
journal= {arXiv preprint arXiv:math/0005208},
year = {2007}
}
Comments
9 pages. To appear in Journal of symbolic Logic