Bulletin of Symbolic Logic

The complexity of classification problems for models of arithmetic

Samuel Coskey and Roman Kossak

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Abstract

We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of arithmetic and for recursively saturated models of arithmetic are Borel; we investigate the precise complexity of each of these. Finally, we show that the classification problem for pairs of recursively saturated models and for automorphisms of a fixed recursively saturated model are Borel complete.

Article information

Source
Bull. Symbolic Logic Volume 16, Issue 3 (2010), 345-358.

Dates
First available: 5 October 2010

Permanent link to this document
http://projecteuclid.org/euclid.bsl/1286284557

Digital Object Identifier
doi:10.2178/bsl/1286284557

Zentralblatt MATH identifier
05806075

Mathematical Reviews number (MathSciNet)
MR2731248

Citation

Coskey, Samuel; Kossak, Roman. The complexity of classification problems for models of arithmetic. Bulletin of Symbolic Logic 16 (2010), no. 3, 345--358. doi:10.2178/bsl/1286284557. http://projecteuclid.org/euclid.bsl/1286284557.


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