Non-tame Mice from Tame Failures of the Unique Branch Hypothesis
Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 903-923
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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.
Mots-clés :
03E15, 03E45, 03E60, mouse, inner model theory, descriptive set theory, hod mouse, core model induction, UBH
Sargsyan, Grigor; Trang, Nam. Non-tame Mice from Tame Failures of the Unique Branch Hypothesis. Canadian journal of mathematics, Tome 66 (2014) no. 4, pp. 903-923. doi: 10.4153/CJM-2013-036-x
@article{10_4153_CJM_2013_036_x,
author = {Sargsyan, Grigor and Trang, Nam},
title = {Non-tame {Mice} from {Tame} {Failures} of the {Unique} {Branch} {Hypothesis}},
journal = {Canadian journal of mathematics},
pages = {903--923},
year = {2014},
volume = {66},
number = {4},
doi = {10.4153/CJM-2013-036-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-036-x/}
}
TY - JOUR AU - Sargsyan, Grigor AU - Trang, Nam TI - Non-tame Mice from Tame Failures of the Unique Branch Hypothesis JO - Canadian journal of mathematics PY - 2014 SP - 903 EP - 923 VL - 66 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-036-x/ DO - 10.4153/CJM-2013-036-x ID - 10_4153_CJM_2013_036_x ER -
%0 Journal Article %A Sargsyan, Grigor %A Trang, Nam %T Non-tame Mice from Tame Failures of the Unique Branch Hypothesis %J Canadian journal of mathematics %D 2014 %P 903-923 %V 66 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-036-x/ %R 10.4153/CJM-2013-036-x %F 10_4153_CJM_2013_036_x
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