Geodesic
Simple structures with complex symmetry
Algebra i logika, Tome 49 (2010) no. 1, pp. 98-134

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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.
Keywords: complexity measure of symmetries of computable structure, automorphism spectrum. 
@article{AL_2010_49_1_a4,
     author = {V. Harizanov and R. Miller and A. S. Morozov},
     title = {Simple structures with complex symmetry},
     journal = {Algebra i logika},
     pages = {98--134},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2010_49_1_a4/}
}
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V. Harizanov; R. Miller; A. S. Morozov. Simple structures with complex symmetry. Algebra i logika, Tome 49 (2010) no. 1, pp. 98-134. http://geodesic.mathdoc.fr/item/AL_2010_49_1_a4/