Predicativity beyond Gamma_0
逻辑
2009-05-11 v3 综合数学
摘要
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 \phi_{\Omega^\omega}(0), and larger ordinals, are predicatively provable.
关键词
引用
@article{arxiv.math/0509244,
title = {Predicativity beyond Gamma_0},
author = {Nik Weaver},
journal= {arXiv preprint arXiv:math/0509244},
year = {2009}
}
备注
38 pages Some minor corrections; no major changes