The complexity of classification problems for models of arithmetic

Details The complexity of classification problems for models of arithmetic The complexity of classification problems for models of arithmetic

2009-08-12

arxiv.org/abs/0908.1718v2

The Bulletin of Symbolic Logic, Volume 16, Number 3, Sept. 2010, pgs 345--358

Mathematics

Logic

15 pages

Scientific paper

10.2178/bsl/1286284557

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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