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Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2014
Footnotes
The first author's work was supported by NSF Grant No DMS-1201348.
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