User blog comment:Vel!/Call for math facts/@comment-5529393-20140730092437

The strengthened finite Ramsey theorem was the first arithmetic statement proven to be independent of PA, proven by Paris and Harrington in 1977.

The function associated with the finite Ramsey theorem has tetrational growth rate, while the function for the strengthened finite Ramsey theorem has the growth rate of f_epsilon_0(n).