A Lipschitz determinacy principle equivalent to weak König lemma

Abstract

RCA0 is a weak subsystem of second order arithmetic which will serve as the base theory. WKL0 is the subsystem of second order arithmetic corresponding to the weak König lemma which states that every infinite tree on {0,1} has an infinite path. (Σ10∧Π10,Δ10)-LDET2 is the principle asserting that one of the two players has a winning strategy in all Lipschitz game with moves from {0,1} such that Player 1 owns a set which is the intersection of an open and a closed subset of 2N in its natural topology and Player 2 owns a clopen subset of 2N. It will be shown that RCA0 proves that WKL0 is equivalent to (Σ10∧Π10,Δ10)-LDET2.