2015 seminar talk: CH and Cofinal maximal chains in the Turing degrees

Talk held by Liang Yu (Nanjing University, Nanjing, PR of China) at the KGRC seminar on 2015-05-28.

Abstract

Over ZFC, we prove that CH is equivalent to the existence of Cofinal maximal chains in the Turing degrees of order type $\omega_1$. However, it is consistent with ZF that they are not equivalent. We also present some applications of the result to the theory of equivalence relations.