On the consistency of the definable tree property on \aleph_1

dc.creatorLeshem, Amir
dc.date2000-05-22
dc.date.accessioned2026-07-07T04:35:25Z
dc.date.available2026-07-07T04:35:25Z
dc.descriptionIn 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 $MA$ 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.
dc.description9 pages. To appear in Journal of symbolic Logic
dc.identifierhttps://arxiv.org/abs/math/0005208
dc.identifierhttp://arxiv.org/abs/math/0005208
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59246
dc.subjectLogic
dc.subjectCombinatorics
dc.titleOn the consistency of the definable tree property on \aleph_1
dc.typetext

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