Mathematical logic seminar - February 3, 2009

Time: 12:00 - 13:20

Room: Baker Hall 150

Speaker:     Spencer Unger    
Department of Mathematical Sciences
Carnegie Mellon University

Title: The tree property


This will be the first in a series of three talks surveying a result due to Mitchell. Namely, Con(ZFC + there is a weakly compact cardinal) implies Con(ZFC + omega_2 has the tree property). In this talk I will state the relevant definitions and background to Mitchell's argument. In particular, I will state, with some sketchy proofs, many relatively easy ways in which the tree property can either hold or fail at a cardinal kappa. I will then survey some of the major results in this line of research, which begins with Mitchell's result. Subsequent talks will be devoted to sketching Mitchell's argument. (Note: This series of talks is designed as a sort of lead up to Itay Neeman's workshop at the end of the month.)