# Over $ZF$, does the existence of a cofinal maximal chain of Turing degrees imply the existence of a well ordering of reals?

BlogOver $ZF$, does the existence of a cofinal maximal chain of Turing degrees imply the existence of a well ordering of reals?

It is known that the existence of a well ordering of Turing degrees imply the existence of a well ordering of reals. And there is a model $M$ of $ZF$ in which there is no well ordering of reals but there is a cofinal chain of Turing degrees.