Nontame mouse from the failure of square at a singular strong limit cardinal
Nontame mouse from the failure of square at a singular strong limit cardinal
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不驯服的老鼠因方在单一强极限基数上的失败
DOI：
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发表时间：
2014
影响因子：
0.9
通讯作者：
G. Sargsyan
中科院分区：
文献类型：
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作者：
G. Sargsyan
在Schimmerling [Coherent sequences and threads，Adv. Math.216（1）（2007）89-117]和Steel [PFA implies ADL（ADL），J. Symbolic Logic 70（4）（2005）1255-1296]的工作基础上，我们证明了平方原理在奇异强极限基数上的失败意味着存在一只非驯服的老鼠。给出的证明是核心模型归纳法中L（θ）以外的第一个归纳步骤，目的是从平方在奇异强极限基数（PFA）处的失效得到AD θ +“Θ是正则的”模型.
Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216(1) (2007) 89–117] and Steel [PFA implies ADL(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 ADℝ + "Θ is regular" from the failure of square at a singular strong limit cardinal or PFA.