Bulletin of Symbolic Logic

The complexity of classification problems for models of arithmetic

Samuel Coskey and Roman Kossak

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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.

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

First available in Project Euclid: 5 October 2010

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

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