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

Speaker: 
Spencer Unger CMU 
Title: 
PCF theory II

Abstract: 
This week I will give the second in a series of talks on PCF Theory. Last week we discussed the idea of ordering functions modulo a filter. We were particularly interested in the case where we had an ultrafilter.
This week we will work in the more general setting of an arbitrary filter, or equivalently its dual ideal. We will address some of the key differences in the two settings (ideal and ultrafilter) and then show how these differences come up in the proof of the Shelah's trichotomy theorem. I will present a sketch proof of the trichotomy theorem and attempt to show how we are essentially trying to reprove the dichotomy theorem in a more general setting. Only this time we have to overcome more difficulties and these difficulties are the result of the differences noted at the beginning of the talk. The notes for the talk will be posted at my logic web page. 