E. Ken

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math.LO2024

Ajtai's theorem for $T_{2}^{2} (R)$ and pebble games with backtracking

Eitetsu Ken, Mykyta Narusevych

We introduce a pebble game extended by backtracking options for one of the two players (called Prover) and reduce the provability of the pigeonhole principle for a generic predicat…

math.LO2024

Games with backtracking options corresponding to the ordinal analysis of $P A$

Eitetsu Ken

We give another proof of ordinal analysis of $I I^£_{k}$ -fragments of Peano Arithmetic which is free from cut-elimination of $I ¨ $ -logic. Our main tool is a direct witnessing argument…

Ajtai's theorem for T22​(R) and pebble games with backtracking

Games with backtracking options corresponding to the ordinal analysis of PA

Ajtai's theorem for $T_{2}^{2} (R)$ and pebble games with backtracking

Games with backtracking options corresponding to the ordinal analysis of $P A$