Series: Penn State Logic Seminar Date: Tuesday, April 19, 2005 Time: 2:30 - 3:45 PM Place: 103 Pond Laboratory Speaker: Carl Mummert, Penn State, Mathematics Title: The Reverse Mathematics of Urysohn's Theorem, part 2 Abstract: Urysohn's Theorem states that a regular, second-countable topological space is metrizable. In Part 1 of this talk, I defined MF spaces and showed that Urysohn's theorem for MF spaces implies Pi^1_2 - CA_0 over Pi^1_1 - CA_0. In Part 2, I will sketch the proof that Urysohn's theorem for MF spaces is provable in Pi^1_2 - CA_0. I will also show that several statements which are classically equivalent to Urysohn's theorem for MF spaces are also equivalent to Pi^1_2 - CA_0 over Pi^1_1 - CA_0. These include ``Every regular countably based MF space is completely metrizable'' and ``Every regular countably based MF space is homeomorphic to a complete separable metric space.''