3 papers
math.LO2021
Computable topological abelian groups
Martino Lupini, Alexander Melnikov, Andre Nies
We study the algorithmic content of Pontryagin - van Kampen duality. We prove that the dualization is computable in the important cases of compact and locally compact totally disco…
math.LO2019
On the complexity of classifying Lebesgue spaces
Tyler Brown, Alexander G. Melnikov, Timothy H. McNicholl
Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.
cs.LO2019
Random Subgroups of Rationals
Ziyuan Gao, Sanjay Jain, Bakhadyr Khoussainov +4
This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup of rationals, two main…