The information content of typical reals
Barmpalias, G. & Lewis-Pye, A.
(2015).
The information content of typical reals.
In
Sommaruga, G. & Strahm, T.
(Eds.),
Turing’s revolution: the impact of his ideas about computability
(pp. 207-224).
Springer Berlin / Heidelberg.
https://doi.org/10.1007/978-3-319-22156-4
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 | Chapter |
|---|---|
| Copyright holders | © 2015 Springer |
| Departments | LSE > Academic Departments > Management |
| DOI | 10.1007/978-3-319-22156-4 |
| Date Deposited | 23 Feb 2016 |
| URI | https://researchonline.lse.ac.uk/id/eprint/65481 |
Explore Further
- http://www.lse.ac.uk/Mathematics/people/Andrew-Lewis-Pye.aspx (Author)
- http://link.springer.com/book/10.1007/978-3-319-22156-4 (Publisher)
- http://www.springer.com/ (Official URL)