Non-tame mice from tame failures of the unique branch hypothesis∗†
نویسنده
چکیده
In this paper, we show that the failure of the unique branch hypothesis (UBH) for tame trees (see Definition 5.1) 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 Steel’s earlier results from [16] for tame trees. In this paper, we establish, using the core model induction, a lower bound for certain failures of the Unique Branch Hypothesis, (UBH), which is the statement that every iteration ∗2000 Mathematics Subject Classifications: 03E15, 03E45, 03E60. †
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Tame Failures of the Unique Branch Hypothesis and Models of Adr + Θ Is Regular
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تاریخ انتشار 2013