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Computability and Randomness$
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André Nies

Print publication date: 2009

Print ISBN-13: 9780199230761

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230761.001.0001

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Higher computability and randomness

Higher computability and randomness

Chapter:
(p.365) 9 Higher computability and randomness
Source:
Computability and Randomness
Author(s):

André Nies

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230761.003.0009

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.

Keywords:   higher computability, Spector–Gandy theorem, Pi-11 randomness, Delta-11 randomness, hyp-dominated set, Delta-11 traceability

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