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

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