41 citations · 45 across the 6 of their papers we have counts for
6 papers
A Note on a Conjecture of Sacks: It is Harder to Embed Height Three Partial Orders than Height Two Partial Orders
Kojiro Higuchi, Patrick Lutz
A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable partial order of size continuum embeds into the Turing degrees. We show that this…
On the order dimension of locally countable partial orderings
Kojiro Higuchi, Steffen Lempp, Diip Raghavan +1
We show that the order dimension of the partial order of all finite subsets of under set inclusion is whenever is an infinite cardinal. We also…
Propagation of partial randomness
Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson +1
Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also…
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…
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…
The degree structure of Weihrauch-reducibility
Kojiro Higuchi, Arno Pauly
We answer a question by Vasco Brattka and Guido Gherardi by proving that the Weihrauch-lattice is not a Brouwer algebra. The computable Weihrauch-lattice is also not a Heyting alge…