In the last few years a series of articles studied computable aspects of learning theory.

2023 - Find a witness or shatter: the landscape of computable PAC learning

2022 - On characterizations of learnability with computable learners

2020 - Decidability of Sample Complexity of PAC Learning in finite setting

2017 - On a learning problem that is independent of the set theory ZFC axioms

2015 - PAC Learning, VC Dimension, and the Arithmetic Hierarchy

2008 - Statistical Learning of Arbitrary Computable Classifiers