Games with backtracking options corresponding to the ordinal analysis of $PA$
| Autor: | Ken, Eitetsu |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 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 |
| Databáze: | arXiv |
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