Non-tame Mice from Tame Failures of the Unique Branch Hypothesis

Sargsyan, Grigor ; Trang, Nam

Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 903-923

Résumé

In this paper, we show that the failure of the unique branch hypothesis $\left( \text{UBH} \right)$ 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 $M\,\vDash \,\text{A}{{\text{D}}^{+}}\,+\,\Theta \,>\,{{\theta }_{0}}$ . 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.

Détail

DOI : 10.4153/CJM-2013-036-x

Mots-clés : 03E15, 03E45, 03E60, mouse, inner model theory, descriptive set theory, hod mouse, core model induction, UBH

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