Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 57, Number 3 (2016), 389-398.
Degrees That Are Not Degrees of Categoricity
A computable structure is -computably categorical for some Turing degree if for every computable structure there is an isomorphism with . A degree is a degree of categoricity if there is a computable structure such that is -computably categorical, and for all , if is -computably categorical, then .
We construct a set whose degree is not a degree of categoricity. We also demonstrate a large class of degrees that are not degrees of categoricity by showing that every degree of a set which is 2-generic relative to some perfect tree is not a degree of categoricity. Finally, we prove that every noncomputable hyperimmune-free degree is not a degree of categoricity.
Notre Dame J. Formal Logic, Volume 57, Number 3 (2016), 389-398.
Received: 2 July 2013
Accepted: 6 February 2014
First available in Project Euclid: 7 April 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03D30: Other degrees and reducibilities
Anderson, Bernard; Csima, Barbara. Degrees That Are Not Degrees of Categoricity. Notre Dame J. Formal Logic 57 (2016), no. 3, 389--398. doi:DOI: 10.1215/00294527-3496154. https://projecteuclid.org/euclid.ndjfl/1460032557