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

Abstract: 
A regular cardinal kappa has the tree property if and only if every kappatree (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 lambdaplus 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. 