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

Grigor Sargsyan

Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA

https://doi.org/10.1142/S0219061314500032Cited by:9 (Source: Crossref)

Abstract

Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216(1) (2007) 89–117] and Steel [PFA implies AD^L(ℝ), J. Symbolic Logic70(4) (2005) 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(ℝ) of the core model induction that is aimed at getting a model of AD_ℝ + "Θ is regular" from the failure of square at a singular strong limit cardinal or PFA.

Keywords:

AMSC: 03E15, 03E45, 03E60

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