Time:  12:30  13:30 
Room: 
Wean Hall 8201

Speaker: 
Xianghui Shi School of Mathematical Sciences Beijing Normal University 
Title: 
Large cardinals and generalized degree structures

Abstract: 
The notion of Turing degree can be generalized to large ordinals, in particular to uncountable cardinals. Sy Friedman showed that in Jensen's constructible universe, the generalized degree structure at singular cardinals of uncountable cofinality is eventually well ordered. I will present an interesting new degree structure at singular cardinals of countable cofinality in the core model for a certain large cardinal. In this talk, I will also discuss the correlation between the complexity of degree structures and the strength of relevant large cardinals. 