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  1.  29
    On the consistency of the definable tree property on ℵ.Amir Leshem - 2000 - Journal of Symbolic Logic 65 (3):1204 - 1214.
    In this paper we prove the equiconsistency of "Every ω 1 -tree which is first order definable over (H ω 1 ·ε) has a cofinal branch" with the existence of a Π 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.
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  2.  29
    The independence of δ1n.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350 - 362.
    In this paper we prove the independence of δ 1 n for n ≥ 3. We show that δ 1 4 can be forced to be above any ordinal of L using set forcing. For δ 1 3 we prove that it can be forced, using set forcing, to be above any L cardinal κ such that κ is Π 1 definable without parameters in L. We then show that δ 1 3 cannot be forced by a set forcing to (...)
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  3.  21
    The Independence of $delta^1_n$.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350-362.
    In this paper we prove the independence of $\delta^1_n$ for n $\geq$ 3. We show that $\delta^1_4$ can be forced to be above any ordinal of L using set forcing. For $\delta^1_3$ we prove that it can be forced, using set forcing, to be above any L cardinal $\kappa$ such that $\kappa$ is $\Pi_1$ definable without parameters in L. We then show that $\delta^1_3$ cannot be forced by a set forcing to be above every cardinal of L. Finally we present (...)
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    The independence of.Amir Leshem & Menachem Magidor - 1999 - Journal of Symbolic Logic 64 (1):350-362.