Suitable Extender Models II: beyond ω-Huge
Suitable Extender Models II: beyond ω-Huge
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DOI：
10.1142/s021906131100102x
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发表时间：
2011-12
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通讯作者：
W. Woodin
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作者：
W. Woodin
我们研究了ω-huge以外的大基数公理在合适扩展器模型的普适性的背景下[j]。日志。10(2010)101-339]。我们证明了在ω-huge的水平上AD的一个类比，更准确地说，AD的最小模型的构造可以推广到Vλ+1的水平。这使我们能够表述AD - l的表示推广，然后证明如果该公理在V中在λ的适当类中成立，那么在每一个适当的扩展器模型中，该公理在λ的适当类中成立（只要可以选择相关的ω-huge嵌入来保持适当的扩展器模型）。
We investigate large cardinal axioms beyond the level of ω-huge in context of the universality of the suitable extender models of [Suitable Extender Models I, J. Math. Log.10 (2010) 101–339]. We show that there is an analog of ADℝ at the level of ω-huge, more precisely the construction of the minimum model of ADℝ generalizes to the level of Vλ+1. This allows us to formulate the indicated generalization of ADℝ and then to prove that if the axiom holds in V at a proper class of λ then in every suitable extender model, the axiom holds at a proper class of λ (provided the relevant ω-huge embeddings can be chosen to preserve the suitable extender model).