Nontame mouse from the failure of square at a singular strong limit cardinal

Journal of Mathematical Logic 14 (1):1450003 (2014)
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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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10.1142/s0219061314500032

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Citations of this work

Simultaneous stationary reflection and square sequences.Yair Hayut & Chris Lambie-Hanson - 2017 - Journal of Mathematical Logic 17 (2):1750010.
Closure properties of measurable ultrapowers.Philipp Lücke & Sandra Müller - 2021 - Journal of Symbolic Logic 86 (2):762-784.
The semi-weak square principle.Maxwell Levine - 2019 - Annals of Pure and Applied Logic 170 (11):102713.

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References found in this work

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.
Core models with more Woodin cardinals.J. R. Steel - 2002 - Journal of Symbolic Logic 67 (3):1197-1226.
Scales in K at the end of a weak gap.J. R. Steel - 2008 - Journal of Symbolic Logic 73 (2):369-390.

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