Mathematical logic seminar – Nov 13 2018

Time: 3:30pm – 4:30 pm

Room: Wean Hall 8220

Speaker: Jing Zhang

Department of Mathematical Sciences

CMU

Title: A Ramsey theorem for (repeated) sums

Abstract:

The motivation is the question: for any finite coloring f: R -> r

does there exist an infinite X such that X + X is monochromatic under f?

Hindman, Leader and Strauss showed the answer is negative if CH holds.

Komjáth, Leader, Russell, Shelah, Soukup and Vidnyánszky showed the

positive answer is consistent relative to the existence of a certain large

cardinal. I will demonstrate how to eliminate the use of large cardinals.

Other variations of the statement will also be discussed, including some

ZFC results.