Jing Zhang : Partition relations and ideal hypothesis

Posted by Tom Benhamou , part of the Logic Seminar.

At

March 7, 2023, 4 p.m.

In

636 SEO

Abstract

We will discuss and address some problems concerning a family of weakenings of the usual Ramsey theorem. Instead of asking for a monochromatic complete graph, very roughly speaking, these versions ask for variations of a monochromatic topological copy of the complete graph, i.e. each edge is replaced by a path. This allows the possibility of consistency at small uncountable cardinals or the continuum where the usual Ramsey theorem is inconsistent. We will also say something about motivation and some recent applications. Joint work with Hrusak and Shelah.