On the consistency of the definable tree property on \aleph_1
| dc.creator | Leshem, Amir | |
| dc.date | 2000-05-22 | |
| dc.date.accessioned | 2026-07-07T04:35:25Z | |
| dc.date.available | 2026-07-07T04:35:25Z | |
| dc.description | 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 $MA$ 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.description | 9 pages. To appear in Journal of symbolic Logic | |
| dc.identifier | https://arxiv.org/abs/math/0005208 | |
| dc.identifier | http://arxiv.org/abs/math/0005208 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59246 | |
| dc.subject | Logic | |
| dc.subject | Combinatorics | |
| dc.title | On the consistency of the definable tree property on \aleph_1 | |
| dc.type | text |