论文标题
超级公理
The Ultrapower Axiom
论文作者
论文摘要
SuperCompact Cardinals的内部模型问题是现代集合理论中的主要开放问题之一，询问是否有一个具有超级型红衣主教的套装理论模型。该问题与强烈紧凑的红衣主教和超级紧凑型红衣主教的等等歧视的更精确的问题密切相关。该论文通过引入一个称为“超能公理的原理”来抽象地解决这两个问题，该原理在所有已知的集合理论的规范模型中都有预期。通过在有超级2型基数的假设下研究超能公理的后果，我们提供了可以解决内部模型问题的证据。此外，我们确定在超能公理下，强大的紧凑性和超紧凑性本质上是等效的。
The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact cardinal. The problem is closely related to the more precise question of the equiconsistency of strongly compact cardinals and supercompact cardinals. This dissertation approaches these two problems abstractly by introducing a principle called the Ultrapower Axiom which is expected to hold in all known canonical models of set theory. By investigating the consequences of the Ultrapower Axiom under the hypothesis that there is a supercompact cardinal, we provide evidence that the inner model problem can be solved. Moreover, we establish that under the Ultrapower Axiom, strong compactness and supercompactness are essentially equivalent.
