What's So Special About Kruskal's Theorem and the Ordinal Gamma0? A Survey of Some Results in Proof Theory

@article{Gallier1991WhatsSS,
  title={What's So Special About Kruskal's Theorem and the Ordinal Gamma0? A Survey of Some Results in Proof Theory},
  author={Jean H. Gallier},
  journal={Ann. Pure Appl. Logic},
  year={1991},
  volume={53},
  pages={199-260}
}
This paper consists primarily of a survey of results of Harvey Friedman about some proof theoretic aspects of various forms of Krusal's tree theorem, and in particular the connection with the ordinal Ƭo. We also include a fairly extensive treatment of normal functions on the countable ordinals, and we give a glimpse of Veblen Hierarchies, some subsystems of second-order logic, slow-growing and fast-growing hierarchies including Girard's result, and Goodstein sequences. The central theme of this… CONTINUE READING

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