In this paper, we show that the failure of the unique branch hypothesis (UBH) for tame trees (see \rdef{ tame iteration tree}) implies that in some homogenous generic extension of $V$ there is a transitive model $M$ containing $Ord \cup \mathbb{ R}$ such that $M\vDash AD^+ + \Theta > \theta_0$. In particular, this implies the existence (in $V$) of a non-tame mouse. The results of this paper significantly extend Steel's earlier results from \cite{ steel2002core} for tame trees.
Categories: math.LO