6 citations · 52 across the 26 of their papers we have counts for
25 papers · 1 filter
Atomic toposes, choice spectra and model-theoretic stability
Takayuki Kihara
For a suitable class of structures , let denote the atomic sheaf topos over the opposite of the category …
The Gamified Katětov order is not linear (in fact, very much not so)
Takayuki Kihara, Ming Ng
Recently, the authors introduced the Gamified Katětov order on filters over . This was shown to be strictly coarser than the classical Katětov order, and in fact collapses all M…
What can Topology tell us about Logical Complexity?
Takayuki Kihara, Ming Ng
In the 1980s, category theorists introduced the Lawvere-Tierney order in the Effective Topos, known to effectively embed the Turing degrees. Understanding it…
Ideal presentations and numberings of some classes of effective quasi-Polish spaces
Matthew de Brecht, Takayuki Kihara, Victor Selivanov
The well known ideal presentations of countably based domains were recently extended to (effective) quasi-Polish spaces. Continuing these investigations, we explore some classes of…
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 open and clopen Ramsey theorems in the Weihrauch lattice
Alberto Marcone, Manlio Valenti
We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to from the…
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…
Degrees of incomputability, realizability and constructive reverse mathematics
Takayuki Kihara
There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of…
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…
Topological reducibilities for discontinuous functions and their structures
Takayuki Kihara
In this article, we give a full description of a topological many-one degree structure of real-valued functions, recently introduced by Day-Downey-Westrick. We also point out that…
Convex choice, finite choice and sorting
Takayuki Kihara, Arno Pauly
We study the Weihrauch degrees of closed choice for finite sets, closed choice for convex sets and sorting infinite sequences over finite alphabets. Our main results are: One, that…
Decomposing functions of Baire class on Polish spaces
Longyun Ding, Takayuki Kihara, Brian Semmes +1
We prove the Decomposability Conjecture for functions of Baire class on a Polish space to a separable metrizable space. This partially answer an important open problem in descr…
On a metric generalization of the -degrees and effective dimension theory
Takayuki Kihara
In this article, we study an analogue of -reducibility for points in computable metric spaces. We characterize the notion of the metric -degree in the context of first-leve…
On the structure of the Wadge degrees of BQO-valued Borel functions
Takayuki Kihara, Antonio Montalbán
In this article, we give a full description of the Wadge degrees of Borel functions from to a better quasi ordering . More precisely, for any countable ordinal $…
Effective forcing with Cantor manifolds
Takayuki Kihara
A set of integers is called total if there is an algorithm which, given an enumeration of , enumerates the complement of , and called cototal if there is an algorithm whi…
The uniform Martin's conjecture for many-one degrees
Takayuki Kihara, Antonio Montalbán
We study functions from reals to reals which are uniformly degree-invariant from Turing-equivalence to many-one equivalence, and compare them "on a cone." We prove that they are in…
Borel-piecewise continuous reducibility for uniformization problems
Takayuki Kihara
We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and -piecewise continuity. Our aim is to understand how a pr…
Turing degrees in Polish spaces and decomposability of Borel functions
Vassilios Gregoriades, Takayuki Kihara, Keng Meng Ng
We give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture for Borel functions on an analytic subset of a Polish space to a sep…
Inside the Muchnik Degrees II: The Degree Structures induced by the Arithmetical Hierarchy of Countably Continuous Functions
Kojiro Higuchi, Takayuki Kihara
It is known that infinitely many Medvedev degrees exist inside the Muchnik degree of any nontrivial subset of Cantor space. We shed light on the fine structures inside thes…
Decomposing Borel functions using the Shore-Slaman join theorem
Takayuki Kihara
Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and…
Inside the Muchnik Degrees I: Discontinuity, Learnability, and Constructivism
Kojiro Higuchi, Takayuki Kihara
Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly comput…