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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  and
Nam Trang
Grigor Sargsyan
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ, 08854 USA. e-mail: grigor@math.rutgers.edu
Nam Trang
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, 15213 USA. e-mail: namtrang@andrew.cmu.edu
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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.

Keywords

03E1503E4503E60mouseinner model theorydescriptive set theoryhod mousecore model inductionUBH

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 66 , Issue 4 , 01 August 2014 , pp. 903 - 923
Copyright
Copyright © Canadian Mathematical Society 2014

Footnotes

*

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

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