On the Consistency of the Definable Tree Property on $\aleph_1$
Leshem, Amir
J. Symbolic Logic, Tome 65 (2000) no. 1, p. 1204-1214 / Harvested from Project Euclid
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In this paper we prove the equiconsistency of "Every $\omega_1$-tree which is first order definable over (H$_{\omega_1}\cdot\varepsilon$) has a cofinal branch" with the existence of 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.
Publié le : 2000-09-14
Classification:  
@article{1183746177,
     author = {Leshem, Amir},
     title = {On the Consistency of the Definable Tree Property on $\aleph\_1$},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 1204-1214},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746177}
}

Leshem, Amir. On the Consistency of the Definable Tree Property on $\aleph_1$. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  1204-1214. http://gdmltest.u-ga.fr/item/1183746177/