Ernest Schimmerling

Mathematical logic seminar - September 15, 2005

Time:	12 - 1:20 p.m.
Room:	OSC 201
Speaker:	James Cummings Associate Professor Department of Mathematical Sciences Carnege Mellon University
Title:	Rainbow Ramsey theory and the PFA continued

Abstract:

A proper poset is a poset which preserves the stationarity of stationary families of countable sets. The Proper Forcing Axiom is the generalisation of Martin's Axiom in which the countable chain condition is weakened to the demand of properness.

In this seminar I plan to

Discuss the characterisation of properness in terms of "generic conditions" for countable elementary submodels
Sketch the theorem that properness is preserved by countable support iteration and also the consistency proof for PFA
Discuss how to force and preserve PFA
Show that a weak consequence of square is consistent with PFA and discuss the consequences of this weakened square