Mathematical logic seminar - October 28, 2008

Time: 12:00 - 13:20

Room: Doherty Hall 4303

Speaker:     James Cummings   
Department of Mathematical Sciences
Carnegie Mellon University

Title: Recent progress on the tree property


A regular cardinal kappa has the tree property if and only if every kappa-tree (tree of height kappa with every level of size less than kappa) has a cofinal branch. This is a basic compactness/reflection property in combinatorial set theory.

A long standing open problem asked whether it is consistent that there is a singular lambda such that lambda-plus has the tree property and the Singular Cardinals Hypothesis fails at lambda: this was recently settled (positively) by Neeman. I'll discuss the background, sketch Neeman's solution, and discuss some open problems.