Time:  12:00  13:20 
Room: 
Doherty Hall 4303

Speaker: 
James Cummings Department of Mathematical Sciences Carnegie Mellon University 
Title: 
The Generalised Continuum Hypothesis and Jensen's diamond principle.

Abstract:  The generalised continuum hypothesis (GCH) is the assertion that for every infinite cardinal kappa, the powerset of kappa has the least possible size (kappaplus). Jensen's diamond principle (diamond at kappaplus) is a strengthening of this assertion which is often useful in building objects of size kappaplus (trees, graphs, colourings, models). Recently Shelah proved that for uncountable kappa these assertions are actually equivalent; I'll give some history and then sketch Shelah's proof. 