Jump to ContentJump to Main Navigation
Computability and Randomness$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

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: 21 October 2021

Lowness properties and K-triviality

Lowness properties and K-triviality

(p.163) 5 Lowness properties and K-triviality
Computability and Randomness

André Nies

Oxford University Press

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .