Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 54, Number 2 (2013), 215-231.
Degrees of Categoricity and the Hyperarithmetic Hierarchy
Barbara F. Csima, Johanna N. Y. Franklin, and Richard A. Shore
Abstract
We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal , is the degree of categoricity of some computable structure . We show additionally that for a computable successor ordinal, every degree -c.e. in and above is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees of categoricity is -complete.
Article information
Source
Notre Dame J. Formal Logic, Volume 54, Number 2 (2013), 215-231.
Dates
First available in Project Euclid: 21 February 2013
Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1361454975
Digital Object Identifier
doi:10.1215/00294527-1960479
Mathematical Reviews number (MathSciNet)
MR3028796
Zentralblatt MATH identifier
1311.03070
Subjects
Primary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Keywords
computability theory computable structure theory Turing degrees isomorphisms
Citation
Csima, Barbara F.; Franklin, Johanna N. Y.; Shore, Richard A. Degrees of Categoricity and the Hyperarithmetic Hierarchy. Notre Dame J. Formal Logic 54 (2013), no. 2, 215--231. doi:10.1215/00294527-1960479. https://projecteuclid.org/euclid.ndjfl/1361454975