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.''