Abstract

Abstract. We reevaluate the claim that predicative reasoning (given the natural numbers) is limited by the Feferman-Schütte ordinal Γ0. First we comprehensively criticize the arguments that have been offered in support of this position. Then we analyze predicativism from first principles and develop a general method for accessing ordinals which is predicatively valid according to this analysis. We find that the Veblen ordinal φΩω(0), and larger ordinals, are predicatively provable. The precise delineation of the extent of predicative reasoning is possibly one of the most remarkable modern results in the foundations of mathematics. Building on

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