|Time:|| 12:30 - 13:50
Wean Hall 8220
Department of Mathematical Sciences
Carnegie Mellon University
Families of universal graphs at successors of singulars
We will discuss the result that for λ a singular cardinal it is possible to have a jointly universal family of graphs on λ+ that has size λ+2 whilst 2λ+=λ+3. Our construction starts with a supercompact cardinal κ and ends by performing either Prikry or Radin forcing to convert κ into the desired singular cardinal. However in between we conduct a preparatory iteration to manipulate the Prikry / Radin names for graphs on κ+ 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.