Time:  3:30pm  4:30 pm 
Room: 
Wean Hall 8220

Speaker: 
James Cummings Department of Mathematical Sciences CMU 
Title: 
Some strong chain conditions

Abstract: 
One of the basic facts in forcing is that a finite support iteration of ccc forcing is ccc. This underlies (for example) the consistency proof for Martin's Axiom. In general an iteration of κclosed κ^{+}cc forcing with <κsupport fails to be κ^{+}cc, and we need strngthened forms of the chain condition. I will discuss some of these strong chain conditions and the corresponding iteration theorems. 