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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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Some advanced computability theory

Some advanced computability theory

(p.238) 6 Some advanced computability theory
Computability and Randomness

André Nies

Oxford University Press

This chapter develops the language of building Turing functionals which is used to characterize promptly simple degrees by low cuppability, and to prove the pseudo-jump inversion theorem of Jockusch and Shore. It provides a new pseudo-jump inversion theorem for Martin–Löf randomness. These results are used to separate highness properties, for instance superhighness from being LR-hard.

Keywords:   Turing functional, promptly simple degree, low cuppability, pseudo-jump inversion, Jockusch and Shore, highness property, superhighness

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