Open Access
2018 Classifications of Computable Structures
Karen Lange, Russell Miller, Rebecca M. Steiner
Notre Dame J. Formal Logic 59(1): 35-59 (2018). DOI: 10.1215/00294527-2017-0015


Let K be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from K such that every structure in K is isomorphic to exactly one structure on the list. Such a list is called a computable classification of K, 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 0'-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 1, even though these families are both closely allied with computable algebraic fields.


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Karen Lange. Russell Miller. Rebecca M. Steiner. "Classifications of Computable Structures." Notre Dame J. Formal Logic 59 (1) 35 - 59, 2018.


Received: 27 June 2014; Accepted: 31 March 2015; Published: 2018
First available in Project Euclid: 30 June 2017

zbMATH: 06848190
MathSciNet: MR3744350
Digital Object Identifier: 10.1215/00294527-2017-0015

Primary: 03C57
Secondary: 03D45

Keywords: computable structure theory , effective classification , equivalence structure , Friedberg enumeration

Rights: Copyright © 2018 University of Notre Dame

Vol.59 • No. 1 • 2018
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