Games with backtracking options corresponding to the ordinal analysis of $PA$

Eitetsu Ken

Games with backtracking options corresponding to the ordinal analysis of $PA$

Logic 2024-09-04 v2

Authors: Eitetsu Ken

Abstract

We give another proof of ordinal analysis of $I\Sigma_{k}$ -fragments of Peano Arithmetic which is free from cut-elimination of $\omega$ -logic. Our main tool is a direct witnessing argument utilizing game notion, motivated from the realm of proof complexity and bounded arithmetic.

Keywords

ordinal analysis Peano Arithmetic game semantics backtracking options proof complexity

Cite

@article{arxiv.2406.17315,
  title  = {Games with backtracking options corresponding to the ordinal analysis of $PA$},
  author = {Eitetsu Ken},
  journal= {arXiv preprint arXiv:2406.17315},
  year   = {2024}
}

Comments

36 pages, figures added, Corollary 4.13 added, revisiting characterization of provably total recursive functions of I\Sigma_k and that of dynamic ordinal analysis are removed for simplicity, presentation improved

Games with backtracking options corresponding to the ordinal analysis of $PA$

Abstract

Keywords

Cite

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