  We examine a version of Ramsey's theorem based on Tao, Gaspar and
Kohlenbach's "finitary" infinite pigeonhole principle.We will show that the
"finitary" infinite Ramsey's theorem naturally gives rise to statements at the
level of the infinite Ramsey's theorem, Friedman's infinite adjacent Ramsey
theorem (well-foundedness of certain ordinals up to $\varepsilon_0$),
$1$-consistency of theories up to PA and the finite Ramsey's theorem.
