Jacob Davis: Families of universal graphs at successors of singulars.

CMU Math Logic Seminar Tuesday 9 September 12:30.   Seminar will meet at 12:30 in Wean Hall 8220.

Speaker: Jacob Davis

Title: Families of universal graphs at successors of singulars.

Abstract:We will discuss the result that for lambda a singular cardinal it is possible
to have a jointly universal family of graphs on lambda^+ that has size
lambda^{+2} whilst 2^{lambda^+}=lambda^{+3}. Our construction starts with a
supercompact cardinal kappa and ends by performing either Prikry or Radin
forcing to convert kappa into the desired singular cardinal. However in between
we conduct a preparatory iteration to manipulate the Prikry / Radin names for
graphs on kappa^+ into a suitable form. In general proving results at
successors of singular cardinals is challenging due to the limited number of
forcing constructions available, so this approach is likely to have wider
applications.

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