Published December 2000
| public
Journal Article
Countable structures with a fixed group of automorphisms
- Creators
- Camerlo, Riccardo
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Kechris, Alexander S.
Chicago
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Abstract
We prove that, given a countable group G, the set of countable structures (for a suitable language L)U_G whose automorphism group is isomorphic to G is a complete coanalytic set and if G ≄ H then U_G is Borel inseparable from U_H . We give also a model theoretic interpretation of this result. We prove, in contrast, that the set of countable structures for L whose automorphism group is isomorphic to ℤ_p^ℕ ,p a prime number, is Π^1_1&Σ^1_1-complete.
Additional Information
© 2000 Springer-Verlag. Received October 25, 1998. We wish to thank R. Dougherty, G. Hjorth, A. Marcone and S. Solecki for their important help and suggestions. In particular A. Marcone helped us in clearing the presentation of the main construction, which is now more perspicuous than in an earlier draft of the paper.Additional details
- Eprint ID
- 38595
- DOI
- 10.1007/BF02773566
- Resolver ID
- CaltechAUTHORS:20130521-095650096
- Created
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2013-05-21Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field