We define the automorphism spectrum of a computable structure \( \mathcal{M} \), a complexity measure of the symmetries of \( \mathcal{M} \), and prove that certain sets of Turing degrees can be realized as automorphism spectra, while certain others cannot.
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*Supported by the NSF (grants DMS-0704256 and DMS-0904101), by the GWU REF award, and by the NSF binational grant DMS-0554841.
**Supported by The City University of New York PSC-CUNY Research Award Program (grant Nos. 60095-34-35, 67182-00-36, 68470-00 37, 69723-00 38, 61467-00 39, and 80209-04-12), by the Templeton Foundation (grant No. 13397), and by the NSF binational grant DMS-0554841.
***Supported by the RFBR (grant Nos. 08-01-00336-a and 09-01-12140-ofi-m) and by the NSF binational grant DMS-0554841.
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Harizanov, V., Miller, R. & Morozov, A.S. Simple structures with complex symmetry. Algebra Logic 49, 68–90 (2010). https://doi.org/10.1007/s10469-010-9079-4
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DOI: https://doi.org/10.1007/s10469-010-9079-4