Abstract
Leo Harrington showed that the second-order theory of arithmetic WKL0 is \({\Pi^1_1}\)-conservative over the theory RCA0. Harrington’s proof is model-theoretic, making use of a forcing argument. A purely proof-theoretic proof, avoiding forcing, has been eluding the efforts of researchers. In this short paper, we present a proof of Harrington’s result using a cut-elimination argument.
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