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

Speaker: 
Jing Zhang Department of Mathematical Sciences CMU 
Title: 
A polarized partition theorem for large saturated linear orders

Abstract: 
Laver proved the following polarized partition theorem for rational numbers: for any natural number d,
any finite coloring f of ℚ^{d}, there exist subsets of ℚ, X_{i} for i < d, each of which has the same order type as
ℚ such that the product X_{0} x ... x X_{d1} gets at most d! many colors. A natural question to ask is what happens when we consider
larger saturated linear orders. We will discuss the consistency at the level of strongly inaccessible cardinals that satisfy some indestructibility property. The
development of versions of the HalpernLäuchli theorem at a large cardinal will be pivotal in the proof.
