Hyperimmunity in 2\sp ℕ

Notre Dame Journal of Formal Logic 48 (2):293-316 (2007)
  Copy   BIBTEX

Abstract

We investigate the notion of hyperimmunity with respect to how it can be applied to Π{\sp 0}{\sb 1} classes and their Muchnik degrees. We show that hyperimmunity is a strong enough concept to prove the existence of Π{\sp 0}{\sb 1} classes with intermediate Muchnik degree—in contrast to Post's attempts to construct intermediate c.e. degrees

Categories

Keywords

Reprint years

DOI

10.1305/ndjfl/1179323269

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 103,343

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Π 1 0 classes, L R degrees and Turing degrees.George Barmpalias, Andrew E. M. Lewis & Frank Stephan - 2008 - Annals of Pure and Applied Logic 156 (1):21-38.
Embeddings into the Medvedev and Muchnik lattices of Π0 1 classes.Stephen Binns & Stephen G. Simpson - 2004 - Archive for Mathematical Logic 43 (3):399-414.
Π 1 0 Classes, Peano Arithmetic, Randomness, and Computable Domination.David E. Diamondstone, Damir D. Dzhafarov & Robert I. Soare - 2010 - Notre Dame Journal of Formal Logic 51 (1):127-159.
Hyperimmunity in 2.Stephen Binns - 2007 - Notre Dame Journal of Formal Logic 48 (2).
Levels of Uniformity.Rutger Kuyper - 2019 - Notre Dame Journal of Formal Logic 60 (1):119-138.
Coding true arithmetic in the Medvedev and Muchnik degrees.Paul Shafer - 2011 - Journal of Symbolic Logic 76 (1):267 - 288.
On the Symmetric Enumeration Degrees.Charles M. Harris - 2007 - Notre Dame Journal of Formal Logic 48 (2):175-204.
Small Π0 1 Classes.Stephen Binns - 2005 - Archive for Mathematical Logic 45 (4):393-410.
Inside the Muchnik degrees II: The degree structures induced by the arithmetical hierarchy of countably continuous functions.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (6):1201-1241.
Mass problems and randomness.Stephen G. Simpson - 2005 - Bulletin of Symbolic Logic 11 (1):1-27.

Analytics

Added to PP
2010-08-24

Downloads
30 (#787,710)

6 months
3 (#1,061,821)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Mass Problems and Intuitionism.Stephen G. Simpson - 2008 - Notre Dame Journal of Formal Logic 49 (2):127-136.
Π⁰₁ classes with complex elements.Stephen Binns - 2008 - Journal of Symbolic Logic 73 (4):1341-1353.
On effectively closed sets of effective strong measure zero.Kojiro Higuchi & Takayuki Kihara - 2014 - Annals of Pure and Applied Logic 165 (9):1445-1469.

Add more citations

References found in this work

No references found.

Add more references