6 citations · 6 across the 4 of their papers we have counts for
5 papers
Modified realizability subtoposes and total Weihrauch reducibility
Akihito Kajikawa, Masamori Kaku, Takayuki Kihara +1
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 ar…
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.…
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…
Many-one reducibility with realizability
Takayuki Kihara
In this article, we propose a new classification of formulas under the realizability interpretation of many-one reducibility (i.e., Levin reducibility). For example, ${\sf…
Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
Takayuki Kihara
We present three different perspectives of oracle. First, an oracle is a blackbox; second, an oracle is a tool to change the way we access mathematical objects; and third, an oracl…