Well, the regular formulation of "Infinitism" is that S is justified to believe P_1 on the basis of P_2 and P_n on the basis of P_n+1. J({regressive, axiomatic}) just defines a limit i.e. S is justified to believe P_1 on the basis of P_2 and P_n on the basis of P_n+1 such that lim_(k->infinity) P_k = P_x where x is not a natural number. You have to say x is not a natural number, because if it were, J's output would have been "foundationalism" and P_x then would be a "self-evident" belief - to use Chisolm's terminology.
P.S. If anyone thinks that this is an abuse of mathematics, I agree. But, its usage is compatible with that of philosophers e.g. Goldman's Causal theory of knowledge literally uses a recursive formulation of belief formation where the base case is "self-evident", I just unwrapped the tail call and wrote it as a loop!