Jing Zhang: A Ramsey theorem for (repeated) sums

Mathematical logic seminar – Oct 30 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.

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