Proof Theory

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The book offers a comprehensive exploration of both classical and intuitionistic predicate logic, significantly expanding upon its predecessor. It introduces the theory of functionals of finite types to elucidate the Gödel interpretation of number theory. Moving away from ramified type theory, it systematically develops classical type theory and predicative analysis. Additionally, it provides consistency proofs for systems of lI~-analysis, employing an innovative notation system for ordinals that enhances previous methodologies.