Thursday, May 3, 2018, from 4 to 5:30pm
East Hall, room 4096
Speaker: Andreas Blass (University of Michigan)
Title: Well-ordered choice implies dependent choice
The axiom of well-ordered choice is a weak form of the axiom of choice. It says that every well-ordered family of nonempty sets has a choice function. The axiom of dependent choice is another weak form of the axiom of choice. It says that, given any directed graph in which every vertex has at least one outgoing arrow, and given any vertex v in that graph, there exists an infinite sequence of vertices that starts at v and then follows the arrows. I’ll prove the old but probably insufficiently well-known theorem of Jensen that well-ordered choice implies dependent choice.