The reverse mathematics of the Thin set and Erdős-Moser theorems

Lu Liu, Ludovic Patey

The thin set theorem for $n$-tuples and $k$ colors (${\mathsf{TS}}_k^n$) states that every $k$-coloring of $[\mathbb{N}{]}^n$ admits an infinite set of integers $H$ such that $[H{]}^n$ a…