Review of An Introduction to Ramsey Theory: Fast Functions, Infinity, and Metamathematics by Matthew Katz and Jan Reimann AMS, 2018 207 pages, Softcover, $52

摘要

The first theorem in Ramsey Theory is: For all 2-colorings of the edges of K_6 there is a monochromatic K_3. This generalizes to the first real theorem: For all m there exists R=R(m) such that, for all 2-colorings of the edges of K_R there is a monochromatic K_m. More generally, Ramsey theory is a branch of combinatorics that deals with statements of the form