Maximal Prikry Sequences
数学专题报告
报告题目(Title)：Maximal Prikry Sequences
报告人(Speaker)：张家铭（卡内基梅隆大学/维也纳工业大学）
地点(Place)：后主楼1225
时间(Time)：2026年4月17日（周五）15:00-16:00
邀请人(Inviter)：施翔晖
报告摘要
In this talk we will investigate the covering machinery of the Jensen-Steel core model K, under the hypothesis that "there is no inner model with a Woodin cardinal". In an earlier work, Mitchell and Schimmerling showed that if ν > ω_2 is a regular cardinal in K but a singular ordinal in V, then ν is a measurable cardinal in K. In this talk we will continue on this route and further show that under a variety of circumstances, there exists a maximal Prikry sequence C for a measure on ν in K. It is proved by Schimmerling that the anti-large cardinal hypothesis is necessary. In a more restrictive setting, we proved that every subset of ν with size < |ν| can be covered by a set in K[C] with size < |ν|. Benhamou and Schimmerling show that the result is optimal. The last part of this talk, we will generalize the proofs in Mitchell's Definable Singularity under the anti-large cardinal hypothesis that "there does not exist an inner model with a Woodin cardinal".
