Meaning of Ramsey theory | Babel Free

Definitions

A branch of mathematics which deals with patterns that inevitably arise in sufficiently large sets (i.e., subsets of some structure).

uncountable

Examples

“Ramsey theory can be loosely described as the study of structure which is preserved under finite decomposition.”

“1999, Randall McCutcheon, Elemental Methods in Ergodic Ramsey Theory, Springer, Lecture Notes in Mathematics: 1722, page 8, We are now ready to offer a loose definition of Ramsey theory. Ramsey theory is a collection of results which, given a finite coloring of some structure, guarantee the existence of certain monochromatic configurations or substructures.”

“In the 35 years since the lectures which form this book were given the area of Ramsey theory has continued to undergo tremendous growth, particularly in the last decade.”

CEFR level