论文标题
最终L和V的某些组合特性
Some combinatorial properties of Ultimate L and V
论文作者
论文摘要
本文在牢固的紧凑性假设下对大型红衣主教的结构建立了许多限制。这些约束与超能公理所施加的约束相吻合，这一原则有望在伍德丁假设的终极\（l \）中保留，为最终\（l \）猜想提供了一些证据。 我们表明，携带不可分解的超级滤器的第一个强度紧凑的每个常规基本主教都是可以衡量的，这为足够大的红衣主教的银色问题回答了一个银色的问题。我们表明，任何接替者几乎紧凑的无数级别级别的基本主教都非常紧凑，这在Boney，Unger和Brooke-Taylor的问题上取得了进展。我们表明，如果有一类适当的紧凑型红衣主教，则没有从集合宇宙中嵌入非平凡的基本基本嵌入到内部模型中，回答了一个批准大型红衣主教的问题。最后，我们表明，如果\（κ\）非常紧凑，则\（v \）是一组强迫内部模型\（κ\ text { - hod} \）的扩展，该集合由由赫生林定义的遗传性定位的集合组成，可从A \（κ\） - 完整的超级级别定义的超级词。 \（κ\ text {-hod} \）似乎是\（v \）的基础的第一个非平地例子，其定义不涉及强迫。
This paper establishes a number of constraints on the structure of large cardinals under strong compactness assumptions. These constraints coincide with those imposed by the Ultrapower Axiom, a principle that is expected to hold in Woodin's hypothesized Ultimate \(L\), providing some evidence for the Ultimate \(L\) Conjecture. We show that every regular cardinal above the first strongly compact that carries an indecomposable ultrafilter is measurable, answering a question of Silver for large enough cardinals. We show that any successor almost strongly compact cardinal of uncountable cofinality is strongly compact, making progress on a question of Boney, Unger, and Brooke-Taylor. We show that if there is a proper class of strongly compact cardinals then there is no nontrivial cardinal preserving elementary embedding from the universe of sets into an inner model, answering a question of Caicedo granting large cardinals. Finally, we show that if \(κ\) is strongly compact, then \(V\) is a set forcing extension of the inner model \(κ\text{-HOD}\) consisting of sets that are hereditarily ordinal definable from a \(κ\)-complete ultrafilter over an ordinal; \(κ\text{-HOD}\) seems to be the first nontrivial example of a ground of \(V\) whose definition does not involve forcing.
