Critical cardinals
Critical cardinals
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关键的红衣主教
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Asaf Karagila
中科院分区：
文献类型：
--
作者：
Yair Hayut;Asaf Karagila
我们引入了临界基数的概念，作为传递集之间足够强的初等嵌入的临界点。假设选择公理，这等价于可测性，但众所周知，选择是等价的必要条件。奇怪的是，这个中心概念以前从未被单独研究过。我们证明了一个技术标准，提升基本嵌入对称扩展，我们用它来表明，它是一致的相对于超紧基数，有一个关键的基数，其继任者是奇异的。
We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the Axiom of Choice this is equivalent to measurability, but it is wellknown that Choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings to symmetric extensions, and we use this to show that it is consistent relative to a supercompact cardinal that there is a critical cardinal whose successor is singular.