Non-tame mice from tame failures of the unique branch hypothesis

Grigor Sargsyan, Nam Trang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we show that the failure of the unique branch hypothesis (UBH) for tame trees implies that in some homogenous generic extension of V there is a transitive model M containing Ord ℝ such that M AD+ + Θ > θ0. 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.

Original languageEnglish (US)
Pages (from-to)903-923
Number of pages21
JournalCanadian Journal of Mathematics
Issue number4
StatePublished - Aug 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Core model induction
  • Descriptive set theory
  • Hod mouse
  • Inner model theory
  • Mouse
  • UBH


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