  Von Mises and Church identified a class of sequences, those with limit frequencies invariant under recursive place selections, that satisfied a number of the measure one stochastic properties of sequences that are thought characteristic of randomness. But the class they identified was too inclusive. The next insight in this area was due to (Martin-Löf 1966), who realised that rather than looking for another single property of sequences that would entail that the sequence met all the further conditions on randomness, it was simpler to adopt as a definition that a sequence is random iff the sequence has all the measure one properties of randomness that can be specified. Here again recursion theory plays a role, for the idea of a measure one property of randomness that can be specified is equivalent to the requirement that there be an effective procedure for testing whether a sequence violates the property. This prompts the following very bold approach to the definition of random sequences: