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Title: Notions and applications of algorithmic randomness
Author: Vermeeren, Stijn
ISNI:       0000 0004 2744 7427
Awarding Body: University of Leeds
Current Institution: University of Leeds
Date of Award: 2013
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Algorithmic randomness uses computability theory to define notions of randomness for infinite objects such as infinite binary sequences. The different possible definitions lead to a hierarchy of randomness notions. In this thesis we study this hierarchy, focussing in particular on Martin-Lof randomness, computable randomness and related notions. Understanding the relative strength of the different notions is a main objective. We look at proving implications where they exists (Chapter 3), as well as separating notions when the are not equivalent (Chapter 4). We also apply our knowledge about randomness to solve several questions about provability in axiomatic theories like Peano arithmetic (Chapter 5).
Supervisor: Cooper, S. B. ; Lewis, A. E. M. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available