Journal of Mathematical Logic 14 (1):1450003 (2014)

Abstract
Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216 89–117] and Steel [PFA implies AD L, J. Symbolic Logic70 1255–1296], we show that the failure of square principle at a singular strong limit cardinal implies that there is a nontame mouse. The proof presented is the first inductive step beyond L of the core model induction that is aimed at getting a model of ADℝ + "Θ is regular" from the failure of square at a singular strong limit cardinal or PFA.
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DOI 10.1142/s0219061314500032
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References found in this work BETA

PFA Implies ADL(R).John R. Steel - 2005 - Journal of Symbolic Logic 70 (4):1255 - 1296.
Characterization of □Κin Core Models.Ernest Schimmerling & Martin Zeman - 2004 - Journal of Mathematical Logic 4 (01):1-72.
The Self-Iterability of L[E].Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (3):751-779.
Scales in K at the End of a Weak Gap.J. R. Steel - 2008 - Journal of Symbolic Logic 73 (2):369-390.
Core Models with More Woodin Cardinals.J. R. Steel - 2002 - Journal of Symbolic Logic 67 (3):1197-1226.

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Citations of this work BETA

Simultaneous Stationary Reflection and Square Sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.
The Semi-Weak Square Principle.Maxwell Levine - 2019 - Annals of Pure and Applied Logic 170 (11):102713.
An Inner Model Proof of the Strong Partition Property for $Delta^{2}_{1}$.Grigor Sargsyan - 2014 - Notre Dame Journal of Formal Logic 55 (4):563-568.

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