Higher computability and randomness
André Nies · Oxford University Press eBooks · 2009
After a brief introduction to higher computability theory, tools from this area are used to obtain mathematical notions of randomness. Many directions from the previous chapters are revisited in this new context. Results often turn out different. For instance, a set that is low for higher Martin–Löf randomness is hyperarithmetical. The chapter studies the strong notion of Pi-11 randomness, which has no counterpart in the classical theory.