The Arithmetical Hierarchy: A Realizability-Theoretic Perspective
Logic
2024-10-22 v1 Logic in Computer Science
Abstract
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical decision problems only plays a role in counting the number of quantifiers, jumps, or mind-changes. In contrast, we reveal that when the realizability interpretation is combined with many-one reducibility, it becomes possible to classify natural arithmetical problems in a very nontrivial way.
Cite
@article{arxiv.2410.15795,
title = {The Arithmetical Hierarchy: A Realizability-Theoretic Perspective},
author = {Takayuki Kihara},
journal= {arXiv preprint arXiv:2410.15795},
year = {2024}
}