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Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
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- Journal:
- Canadian Journal of Mathematics / Volume 66 / Issue 4 / 01 August 2014
- Published online by Cambridge University Press:
- 20 November 2018, pp. 903-923
- Print publication:
- 01 August 2014
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- Article
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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.
