Tame failures of the unique branch hypothesis and models of ADℝ + Θ is regular

Journal of Mathematical Logic 16 (2):1650007 (2016)
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Abstract

In this paper, we show that the failure of the unique branch hypothesis for tame iteration trees implies that in some homogenous generic extension of [Formula: see text] there is a transitive model [Formula: see text] containing [Formula: see text] such that [Formula: see text] is regular. The results of this paper significantly extend earlier works from [Non-tame mice from tame failures of the unique branch bypothesis, Canadian J. Math. 66 903–923; Core models with more Woodin cardinals, J. Symbolic Logic 67 1197–1226] for tame trees.

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References found in this work

Suitable extender models I.W. Hugh Woodin - 2010 - Journal of Mathematical Logic 10 (1):101-339.
PFA Implies ADL(R).John R. Steel - 2005 - Journal of Symbolic Logic 70 (4):1255 - 1296.
Inner models in the region of a Woodin limit of Woodin cardinals.Itay Neeman - 2002 - Annals of Pure and Applied Logic 116 (1-3):67-155.
Core models with more Woodin cardinals.J. R. Steel - 2002 - Journal of Symbolic Logic 67 (3):1197-1226.

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