For a class of sets, let us say that a set A is stabilising if for every . We prove that the Martin–Löf stabilising sets are exactly the K-trivial sets, as are the weakly 2-random stabilising sets. We also show that the 1-generic stabilising sets are exactly the computable sets.
The first author was partially supported by John Templeton Foundation grant 15619: “Mind, Mechanism and Mathematics: Turing Centenary Research Project”.