- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Mass problems and density
Journal of Mathematical Logic 16 (2):1650006 (2016)
Abstract
Recall that [Formula: see text] is the lattice of Muchnik degrees of nonempty effectively compact sets in Euclidean space. We solve a long-standing open problem by proving that [Formula: see text] is dense, i.e. satisfies [Formula: see text]. Our proof combines an oracle construction with hyperarithmetical theory.Other Versions
No versions found
Links
PhilArchive
External links
(no proxy)
Setup an account with your affiliations in order to access resources via your University's proxy server
Through your library
- Sign in / register and customize your OpenURL resolver
- Configure custom resolver
My notes
Similar books and articles
Mass problems and hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
Ramsey’s theorem for pairs, collection, and proof size.Leszek Aleksander Kołodziejczyk, Tin Lok Wong & Keita Yokoyama - 2023 - Journal of Mathematical Logic 24 (2).
The mouse set theorem just past projective.Mitch Rudominer - forthcoming - Journal of Mathematical Logic.
Degrees containing members of thin Π10 classes are dense and co-dense.Rodney G. Downey, Guohua Wu & Yue Yang - 2018 - Journal of Mathematical Logic 18 (1):1850001.
Bounds on Scott ranks of some polish metric spaces.William Chan - 2020 - Journal of Mathematical Logic 21 (1):2150001.
Games with filters I.Matthew Foreman, Menachem Magidor & Martin Zeman - 2023 - Journal of Mathematical Logic 24 (3).
On the definability of the double jump in the computably enumerable sets.Peter A. Cholak & Leo A. Harrington - 2002 - Journal of Mathematical Logic 2 (02):261-296.
The equivalence of Axiom (∗)+ and Axiom (∗)++.W. Hugh Woodin - forthcoming - Journal of Mathematical Logic.
On cuts in ultraproducts of linear orders I.Mohammad Golshani & Saharon Shelah - 2016 - Journal of Mathematical Logic 16 (2):1650008.
Analytics
Added to PP
2019-07-15
Downloads
20 (#1,084,435)
6 months
4 (#864,415)
2019-07-15
Downloads
20 (#1,084,435)
6 months
4 (#864,415)
Historical graph of downloads
References found in this work
A splitting theorem for the Medvedev and Muchnik lattices.Stephen Binns - 2003 - Mathematical Logic Quarterly 49 (4):327.
Density of the Medvedev lattice of Π0 1 classes.Douglas Cenzer & Peter G. Hinman - 2003 - Archive for Mathematical Logic 42 (6):583-600.
Mass problems and hyperarithmeticity.Joshua A. Cole & Stephen G. Simpson - 2007 - Journal of Mathematical Logic 7 (2):125-143.
Coding true arithmetic in the Medvedev and Muchnik degrees.Paul Shafer - 2011 - Journal of Symbolic Logic 76 (1):267 - 288.
A recursively enumerable degree which will not split over all lesser ones.Alistair H. Lachlan - 1976 - Annals of Mathematical Logic 9 (4):307.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-8567d8d854-zpjm8 dc2