Thin set theorem for arbitrarily many colors implies bounding

Yamato Miyata, Keita Yokoyama

The thin set theorem ${\mathsf{RT}}_{<\infty ,\ell }^n$ asserts that for every natural number $k$, each coloring $c:[\mathbb{N}{]}^n\to \{0,1,\dots ,k-1\}$ admits an infinite set…