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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 29 November 2021

Higher computability and randomness

Higher computability and randomness

(p.365) 9 Higher computability and randomness
Computability and Randomness

André Nies

Oxford University Press

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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