5 citations · 12 across the 7 of their papers we have counts for
13 papers
On some topics around the Wadge rank
Takayuki Kihara
Kechris and Martin showed that the Wadge rank of the -th level of the decreasing difference hierarchy of coanalytic sets is under the axiom of determinacy. In this article…
Lawvere-Tierney topologies for computability theorists
Takayuki Kihara
In this article, we introduce certain kinds of computable reduction games with imperfect information. One can view such a game as an extension of the notion of Turing reduction, an…
A syntactic approach to Borel functions: Some extensions of Louveau's theorem
Takayuki Kihara, Kenta Sasaki
Louveau showed that if a Borel set in a Polish space happens to be in a Borel Wadge class , then its -code can be obtained from its Borel code in a hyperarithmetical manner.…
The Brouwer invariance theorems in reverse mathematics
Takayuki Kihara
In his book, John Stillwell wrote "finding the exact strength of the Brouwer invariance theorems seems to me one of the most interesting open problems in reverse mathematics." In t…
Wadge-like degrees of Borel bqo-valued functions
Takayuki Kihara, Victor Selivanov
We unite two well known generalisations of the Wadge theory. The first one considers more general reducing functions than the continuous functions in the classical case, and the se…
A comparison of various analytic choice principles
Paul-Elliot Anglès d'Auriac, Takayuki Kihara
We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing detailed analysis of the Medvedev lattice…