Freiburg Research Seminar in Mathematical Logic talk: Cardinal characteristics at supercompact kappa in the small u(kappa), large 2^kappa model

Andrew D Brooke-Taylor (Speaker)

Activity: Participating in or organising an event typesInvited talk

Description

Freiburg Research Seminar in Mathematical Logic talk: Cardinal characteristics at supercompact kappa in the small u(kappa), large 2^kappa model

Abstract: When generalising arguments about cardinal characteristics of the continuum to cardinals kappa greater than omega, one frequently comes up against the problem of how to ensure that a filter built up through an iterated forcing remains kappa complete at limit stages of small cofinality. A technique of Dzamonja and Shelah is useful for overcoming this problem; in particular, there is a natural application of this technique to obtain a model in which 2^kappa is large but the ultrafilter number u(kappa) is kappa^+. After introducing this model, I will talk about joint work with Vera Fischer (Technical University of Vienna) and Diana Montoya (University of Vienna) calculating many other cardinal characteristics at kappa in the model and its variants.
Period14 Jan 2015
Event typeConference

Keywords

  • set theory
  • large cardinal axioms