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Random reals and Lipschitz continuity

Lewis-Pye, Andrew and Barmpalias, George (2006) Random reals and Lipschitz continuity. Mathematical Structures in Computer Science, 16 (5). pp. 737-749. ISSN 0960-1295

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Identification Number: 10.1017/S0960129506005445


Lipschitz continuity is used as a tool for analysing the relationship between incomputability and randomness. We present a simpler proof of one of the major results in this area – the theorem of Yu and Ding, which states that there exists no cl-complete c.e. real – and go on to consider the global theory. The existential theory of the cl degrees is decidable, but this does not follow immediately by the standard proof for classical structures, such as the Turing degrees, since the cl degrees are a structure without join. We go on to show that strictly below every random cl degree there is another random cl degree. Results regarding the phenomenon of quasi-maximality in the cl degrees are also presented.

Item Type: Article
Official URL:
Additional Information: © 2006 Cambridge University Press
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 06 Aug 2013 11:12
Last Modified: 16 May 2024 00:32

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