Predicativity beyond Gamma_0

Nik Weaver

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Predicativity beyond Gamma_0

Nik Weaver

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Abstract

We reevaluate the claim that predicative reasoning (given the natural numbers) is limited by the Feferman-Schutte ordinal Gamma_0. 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 ϕ_{Ω^ω}(0), and larger ordinals, are predicatively provable.

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BibTeX RIS

Nik Weaver. 2009-05-11. Predicativity beyond Gamma_0. https://arxiv.org/abs/math/0509244

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