论文标题
可测量超级能的闭合特性
Closure properties of measurable ultrapowers
论文作者
论文摘要
我们研究了Hamkin的“新鲜度”概念的可测量超能力的闭合性质，并表明这些特性的程度高度取决于集合理论的基础模型的组合特性。在一个方向上，Sakai的结果表明，通过将强烈紧凑的红衣主教折叠成为可测量的基本主教的双重后继者，就可以获得一个集体理论模型，在该模型中，这种超能力具有最强的封闭特性。在另一个方向上，我们使用各种平方原理来表明规范内部模型的可测量超级能力仅具有最少的闭合性能。此外，这些结果的证明中开发的技术还使我们能够得出有关具有非最小闭合性能的可测量超能力的一致性强度的陈述。
We study closure properties of measurable ultrapowers with respect to Hamkin's notion of "freshness" and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one direction, a result of Sakai shows that, by collapsing a strongly compact cardinal to become the double successor of a measurable cardinal, it is possible to obtain a model of set theory in which such ultrapowers possess the strongest possible closure properties. In the other direction, we use various square principles to show that measurable ultrapowers of canonical inner models only possess the minimal amount of closure properties. In addition, the techniques developed in the proofs of these results also allow us to derive statements about the consistency strength of the existence of measurable ultrapowers with non-minimal closure properties.
