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The information content of typical reals

Barmpalias, George and Lewis-Pye, Andy (2015) The information content of typical reals. In: Sommaruga, Giovanni and Strahm, Thomas, (eds.) Turing’s revolution: the impact of his ideas about computability. Springer, pp. 207-224. ISBN 9783319221557

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Identification Number: 10.1007/978-3-319-22156-4

Abstract

The degrees of unsolvability provide a way to study the continuum in algorithmic terms. Measure and category, on the other hand, provide notions of size for subsets of the continuum, giving rise to corresponding notions of “typicality” for real numbers. We give an overview of the order-theoretic properties of the degrees of typical reals, presenting old and recent results, and pointing to a number of open problems for future research on this topic.

Item Type: Book Section
Official URL: http://www.springer.com/
Additional Information: © 2015 Springer
Subjects: Q Science > QA Mathematics
Sets: Departments > Management
Date Deposited: 23 Feb 2016 09:55
Last Modified: 23 Feb 2016 09:55
URI: http://eprints.lse.ac.uk/id/eprint/65481

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