Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume's Principle, which says that the number of Fs is identical to the number of Gs if and on...
Leo Harrington showed that the second-order theory of arithmetic WKL0 is 1 1-conservative over the theory RCA0. Harrington's proof is model-theoretic, making use of a forcing...