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Descripción

Let $\mathcal{K}$ be a family of structures, closed under isomorphism, in a fixed computable language. We consider effective lists of structures from $\mathcal{K}$ such that every structure in $\mathcal{K}$ is isomorphic to exactly one structure on the list. Such a list is called a computable classification of $\mathcal{K}$ , 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 $\mathbf{0'}$ -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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Project Euclid (Hosted at Cornell University Library)  

Autor(es)

Lange, Karen -  Miller, Russell -  Steiner, Rebecca M. - 

Id.: 70828091

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveFriedberg enumeration - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 University of Notre Dame

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0029-4527
[References] 1939-0726

Fecha de contribución: 06-ene-2018

Contacto:

Localización:
* Notre Dame J. Formal Logic 59, no. 1 (2018), 35-59
* doi:10.1215/00294527-2017-0015

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