AXIOMS FOR GROUNDED TRUTH

We axiomatize Leitgeb’s (2005) theory of truth and show that this theory proves all arithmetical sentences of the system of ramified analysis up to e0. We also give alternative axiomatizations of Kripke’s (1975) theory of truth (Strong Kleene and supervaluational version) and show that they are at least as strong as the Kripke-Feferman system KF and Cantini’s VF, respectively.