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Search: MSC category 03E45 ( Inner models, including constructibility, ordinal definability, and core models )

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1. CJM 2013 (vol 66 pp. 903)

Sargsyan, Grigor; Trang, Nam
Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
In this paper, we show that the failure of the unique branch hypothesis (UBH) for tame trees implies that in some homogenous generic extension of $V$ there is a transitive model $M$ containing $Ord \cup \mathbb{R}$ such that $M\vDash \mathsf{AD}^+ + \Theta \gt \theta_0$. In particular, this implies the existence (in $V$) of a non-tame mouse. The results of this paper significantly extend J. R. Steel's earlier results for tame trees.

Keywords:mouse, inner model theory, descriptive set theory, hod mouse, core model induction, UBH
Categories:03E15, 03E45, 03E60

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