Kojiro Higuchi

The degree structure of Weihrauch-reducibility

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 algebra, but the continuous Weihrauch-lattice is. We further investigate the existence of infinite infima and suprema, as well as embeddings of the Medvedev-degrees into the Weihrauch-degrees.

Inside the Muchnik degrees I: Discontinuity, learnability and constructivism

Every computable function has to be continuous. To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space. First, we classify nonuniformly computable functions on Baire space from the viewpoint of learning theory and piecewise computability. For instance, we show that mind-change-bounded-learnability is equivalent to finite

Propagation of partial randomness

(\Pi^0_1)_2

On effectively closed sets of effective strong measure zero

-piecewise computability (where

Effectively closed mass problems and intuitionism

(\Pi^0_1)_2

Effective strong nullness and effectively closed sets

denotes the difference of two

On the strength of marriage theorems and uniformity

\Pi^0_1

On Values of Games

sets), error-bounded-learnability is equivalent to finite

Defining a randomness notion via another

\Delta^0_2

Weak theories of concatenation and minimal essentially undecidable theories

-piecewise computability, and learnability is equivalent to countable