|Time:|| 12:00 - 13:20
Doherty Hall 4303
Department of Mathematical Sciences
Carnegie Mellon University
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 (kappa-plus). Jensen's diamond principle (diamond at kappa-plus) is a strengthening of this assertion which is often useful in building objects of size kappa-plus (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.|