The Information Content of Typical Reals

George Barmpalias () and Andy Lewis-Pye ()
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George Barmpalias: Institute of Software, Chinese Academy of Sciences, State Key Lab of Computer Science
Andy Lewis-Pye: London School of Economics, Department of Mathematics, Columbia House

A chapter in Turing’s Revolution, 2015, pp 207-224 from Springer

Abstract: 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.

Keywords: Category; Genericity; Measure; Randomness; Turing degrees (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22156-4_8

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DOI: 10.1007/978-3-319-22156-4_8

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