In a contest on the XKCD forums to name the largest well-defined computable integer, Eliezer Yudkowsky submitted: Let T be the first-order theory of Zermelo-Fraenkel set theory plus the Axiom of Choice plus the axiom that there exists an I0 rank-into-rank cardinal. This is the most powerful known large cardinal axiom, AFAIK. I think that one such cardinal implies the existence of an infinite number of them, but if not, consider that condition added. Starting with P = 10: Repeat 10 times.