Reverse mathematics of a color basis theorem

Abstract

The infinite pigeonhole theorem asserts that if $f:\mathbb{N}\to m$ is a function with a finite range, then there is a $j<m$ such that the set $\{n\in \mathbb{N}\mid f(n)=j\}$ is infinite. This article uses the techniques of reverse mathematics and Weihrauch analysis to examine the strength of a theorem that finds all the values that occur infinitely often in the range of a function.