Hydra games for recursively Mahlo operations

TL;DR

This paper introduces a hydra game model and proves its termination is equivalent to the 1-consistency of set theory KPM for recursively Mahlo universes, linking game theory with foundational set theory.

Contribution

It establishes a novel connection between hydra game termination and the 1-consistency of a specific set theory involving recursively Mahlo universes.

Findings

Hydra games always terminate.

Termination is equivalent to 1-consistency of KPM.

Links game theory with set-theoretic consistency.

Abstract

A hydra game is proposed, and the fact that every hydra eventually die out is shown to be equivalent (over a weak arithmetic) to the 1-consistency of set theory KPM for recursively Mahlo universes.