Modified realizability subtoposes and total Weihrauch reducibility

Akihito Kajikawa; Masamori Kaku; Takayuki Kihara; Satoshi Nakata

Modified realizability subtoposes and total Weihrauch reducibility

Logic 2026-08-03 v1 Logic in Computer Science

Authors: Akihito Kajikawa , Masamori Kaku , Takayuki Kihara , Satoshi Nakata

Abstract

In recent years, there has been rapid development in the foundational study of oracle computability from the perspective of Lawvere-Tierney topologies and their sheaves. In this article, we formulate and analyze the notion of reducibility within the framework of total computability. Then, using sheaf subtoposes derived from oracles in the total computable setting, we establish separations between various hierarchies of logical principles, including the hierarchies of the weak law of excluded middle $\mathbf{WLEM}$ , the lessor limited principle of omniscience $\mathbf{LLPO}$ , and Markov's principle $\mathbf{MP}$ .

Cite

@article{arxiv.2608.02133,
  title  = {Modified realizability subtoposes and total Weihrauch reducibility},
  author = {Akihito Kajikawa and Masamori Kaku and Takayuki Kihara and Satoshi Nakata},
  journal= {arXiv preprint arXiv:2608.02133},
  year   = {2026}
}