Archive for Mathematical Logic 43 (3):327-336 (2004)

Abstract
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see whether some classes whose set of countable members is very complex become classifiable when we consider only computable members. We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. For real closed fields we show that the isomorphism problem is Δ1 1 complete (the maximum possible), and for others we show that it is of relatively low complexity. We show that the isomorphism problem for algebraically closed fields, Archimedean real closed fields, or vector spaces is Π0 3 complete
Keywords Mathematics
Categories (categorize this paper)
DOI 10.1007/s00153-004-0219-1
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,316
Through your library

References found in this work BETA

Recursively Enumerable Vector Spaces.G. Metakides - 1977 - Annals of Mathematical Logic 11 (2):147.
Effective Content of Field Theory.G. Metakides - 1979 - Annals of Mathematical Logic 17 (3):289.

Add more references

Citations of this work BETA

Scott Sentences for Certain Groups.Julia F. Knight & Vikram Saraph - 2018 - Archive for Mathematical Logic 57 (3-4):453-472.
Classification From a Computable Viewpoint.Wesley Calvert & Julia F. Knight - 2006 - Bulletin of Symbolic Logic 12 (2):191-218.

View all 8 citations / Add more citations

Similar books and articles

Isomorphism of Homogeneous Structures.John D. Clemens - 2009 - Notre Dame Journal of Formal Logic 50 (1):1-22.
Effectively Closed Sets and Enumerations.Paul Brodhead & Douglas Cenzer - 2008 - Archive for Mathematical Logic 46 (7-8):565-582.
Computable Embeddings and Strongly Minimal Theories.J. Chisholm, J. F. Knight & S. Miller - 2007 - Journal of Symbolic Logic 72 (3):1031 - 1040.
A Model Theoretical Generalization of Steinitz’s Theorem.Alexandre Martins Rodrigues & Edelcio De Souza - 2011 - Principia: An International Journal of Epistemology 15 (1):107-110.
Effective Algebraicity.Rebecca M. Steiner - 2013 - Archive for Mathematical Logic 52 (1-2):91-112.
Finite Computable Dimension Does Not Relativize.Charles F. D. McCoy - 2002 - Archive for Mathematical Logic 41 (4):309-320.
Analytic Equivalence Relations and Bi-Embeddability.Sy-David Friedman & Luca Motto Ros - 2011 - Journal of Symbolic Logic 76 (1):243 - 266.

Analytics

Added to PP index
2013-11-23

Total views
16 ( #668,647 of 2,519,507 )

Recent downloads (6 months)
1 ( #407,153 of 2,519,507 )

How can I increase my downloads?

Downloads

My notes