The Discontinuity Problem

Abstract: We introduce the discontinuity problem and we prove that under the axiom of determinacy it is actually the weakest discontinuous problem in the topological Weihrauch lattice. We also discuss algebraic properties of the discontinuity problem, such as the fact that it parallelizes to the non-computability problem. We also introduce an operation that we call stashing and show that is dual to parallelization. We show that the discontinuity problem is the stashing of LLPO and several variants of it.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

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