Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 59, Number 1 (2018), 35-59.
Classifications of Computable Structures
Let be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from such that every structure in is isomorphic to exactly one structure on the list. Such a list is called a computable classification of , up to isomorphism. Using the technique of Friedberg enumeration, we show that there is a computable classification of the family of computable algebraic fields and that with a -oracle, we can obtain similar classifications of the families of computable equivalence structures and of computable finite-branching trees. However, there is no computable classification of the latter, nor of the family of computable torsion-free abelian groups of rank , even though these families are both closely allied with computable algebraic fields.
Notre Dame J. Formal Logic, Volume 59, Number 1 (2018), 35-59.
Received: 27 June 2014
Accepted: 31 March 2015
First available in Project Euclid: 30 June 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03C57: Effective and recursion-theoretic model theory [See also 03D45]
Secondary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
Lange, Karen; Miller, Russell; Steiner, Rebecca M. Classifications of Computable Structures. Notre Dame J. Formal Logic 59 (2018), no. 1, 35--59. doi:10.1215/00294527-2017-0015. https://projecteuclid.org/euclid.ndjfl/1498788255