Starting with two supercompact cardinals we produce a generic extension of the universe in which a principle that we call GM+(ω 3,ω1) holds. This principle implies ISP(ω2) and ISP(ω3), and hence the tree property at ω2 and ω3, the Singular Cardinal Hypothesis, and the failure of the weak square principle □(ω2,λ), for all regular λ ≥ ω2. In addition, it implies that the restriction of the approachability ideal I[ω2] to the set of ordinals of cofinality ω1 is the nonstationary ideal on this set. The consistency of this last statement was previously shown by W. Mitchell.

中文翻译：

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猜测模型和可接近性理想

从两个超紧致红衣主教开始，我们产生了宇宙的一般扩展，其中我们称之为原理通用汽车+(ω 3,ω1)持有。这一原则意味着互联网服务提供商(ω2)和互联网服务提供商(ω3)，因此树属性在ω2和ω3，奇异基数假设和弱平方原理的失败□(ω2,λ), 对于所有正则λ ≥ ω2. 此外，这意味着可接近性理想的限制一世[ω2]到共尾序数集ω1是这个集合上的非平稳理想。W. Mitchell 之前已经证明了最后一个陈述的一致性。