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

Published online by Cambridge University Press:  20 November 2018

Grigor Sargsyan
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ, 08854 USA. e-mail: [email protected]
Nam Trang
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213 USA. e-mail: [email protected]
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

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The first author's work was supported by NSF Grant No DMS-1201348.

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