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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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Lowness properties and K-triviality

Lowness properties and K-triviality

Chapter:
(p.163) 5 Lowness properties and K-triviality
Source:
Computability and Randomness
Author(s):

André Nies

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230761.003.0005

This chapter shows the equivalence of K-triviality and lowness for Martin–Löf randomness. This coincidence extends to other lowness properties, such as being a base for Martin–Löf randomness, and lowness for weak 2-randomness. To prove the results, the chapter develops the accounting, cost function and decanter methods, and the golden run construction. The Main Lemma, derived from the golden run construction, yields a general way to restrict K-trivial sets.

Keywords:   lowness properties, Martin–Löf, base for Martin–Löf randomness, cost function, K-triviality, weak 2-randomness, Main Lemma, decanter method, golden run

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