TL;DR
This paper introduces a hydra battle concept demonstrating that, within certain set theories, the termination of hydra battles cannot be proven, highlighting limitations of these theories in formalizing such processes.
Contribution
It presents a new hydra battle model showing unprovability results in set theories with urelements and uncountable regular ordinals.
Findings
Hydra battles always terminate in the model.
Termination is unprovable in the specified set theory.
Highlights limitations of formal systems in proving termination.
Abstract
In this paper we introduce a hydra battle. Each hydra will eventually die out, but the fact is not provable in a set theory with urelements of natural numbers and the assumption that `there exists an uncountable regular ordinal'.
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Taxonomy
TopicsComputability, Logic, AI Algorithms