2 papers
math.LO2026
The Game-Theoretic Katětov Order and Idealised Effective Subtoposes
Takayuki Kihara, Ming Ng
This paper addresses the longstanding problem of determining the structure of the -order in the Effective Topos, known to effectively embed the Turing degrees.…
math.LO2024
The Arithmetical Hierarchy: A Realizability-Theoretic Perspective
Takayuki Kihara
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the n…