Contents

Monochromatic Structures in Colorings of the Positive Integers and the Finite Subsets of the Positive Integers

Tom C. Brown1
1Department of Mathematics Simon Fraser University Burnaby, BC, Canada V5A 186

Abstract

We discuss van der Waerden’s theorem on arithmetic progressions and an extension using Ramsey’s theorem, and the canonical versions. We then turn to a result (Theorem 6 below) similar in character to van der Waerden’s theorem, applications of Theorem 6, and possible canonical versions of Theorem 6. We mention several open questions involving arithmetic progressions and other types of progressions.