Ernest Schimmerling

Mathematical logic seminar - September 5, 2006

Time: 12 - 1:20 p.m.

Room: WH 5304

Speaker:     James Cummings   
Department of Mathematical Sciences
Carnegie Mellon University

Title: Generic ultrapowers

Abstract: The speaker will finish going over prerequisites for the upcoming Appalachian set theory workshop, starting with:

Define NSω1 to be ω2-saturated if there is no sequence of stationary sets, Sα for α<ω2, such that Sα∩Sβ is non-stationary for distinct α,β < ω2.

Assume that NSω1 is ω2-saturated and force with it to obtain a V-generic filter G. Then,

  • if M is the Mostowski collapse of ult(V,G), then M is transitive,
  • if j is the natural elementary embedding of V into M, then

    j(ω1V) = ω1M = ω1V[G] = ω2V

  • M is countably closed in V[G]