具有回溯选项的博弈论述及其对应于$PA$的序数分析
逻辑
2024-09-04 v2
摘要
我们给出一种无需对逻辑进行剪枝即可进行中片段序数分析的另一种证明方法。我们的主要工具是一种直接的见证论证，利用博弈概念，这一概念是从证明复杂度和有界算术领域中激发的。
引用
@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}
}
备注
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