Geodesic
Simple structures with complex symmetry
Algebra i logika, Tome 49 (2010) no. 1, pp. 98-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Dimitrov R., Harizanov V., Morozov A., “Dependence relations in computably rigid computable vector spaces”, Ann. Pure Appl. Logic, 132:1 (2005), 97–108 | DOI | MR | Zbl

[2] Morozov A. S., “Zhestkie konstruktivnye moduli”, Algebra i logika, 28:5 (1989), 570–583 | MR | Zbl

[3] Hirschfeldt D. R., Khoussainov B., Shore R. A., Slinko A. M., “Degree spectra and computable dimensions in algebraic structures”, Ann. Pure Appl. Logic, 115:1–3 (2002), 71–113 | DOI | MR | Zbl

[4] Soare R. I., Recursively enumerable sets and degrees, A study of computable functions and computably generated sets, Springer-Verlag, Berlin, 1987 ; R. I. Soar, Vychislimo perechislimye mnozhestva i stepeni. Izuchenie vychislimykh funk- tsii i vychislimo perechislimykh mnozhestv, Kazanskoe matem. ob-vo, Kazan, 2000 | MR | MR | Zbl

[5] Marker D., “Non $\Sigma_n$ axiomatizable almost strongly minimal theories”, J. Symb. Log., 54:3 (1989), 921–927 | DOI | MR | Zbl

[6] Fokina E., Kalimullin I., Miller R. G., Degrees of categoricity of computable structures (to appear)

[7] Kreisel G., Shoenfield J., Wang H., “Number theoretic concepts and recursive well-orderings”, Arch. Math. Logik Grundlagenforsch, 5 (1961), 42–64 | DOI | MR | Zbl

[8] Hirschfeldt D. R., unpublished result

[9] Schmerl J., unpublished result

[10] Kueker D. W., “Definability, automorphisms, and infinitary languages”, Syntax Semantics infinit. Languages (Symposium Ucla, 1967), Lect. Notes Math., 72, ed. J. Barwise, Springer-Verlag, Berlin, 1968, 152–165 | MR

[11] Jockusch C. G. (jun.), McLaughlin T. G., “Countable retracing functions and $\Pi^0_2$ predicates”, Pac. J. Math., 30 (1969), 67–93 | MR | Zbl

[12] Odifreddi P. G., Classical recursion theory, v. II, Studies Logic Found. Math., 143, North-Holland, Amsterdam, 1999 | MR

[13] Morozov A. S., “Groups of computable automorphisms”, Handbook of recursive mathematics, v. 1, Stud. Logic Found. Math., 138, North-Holland, Amsterdam, 1998, 311–345 | MR

[14] Sacks G. E., Higher type recursion theory, Perspect. Math. Log., Springer-Verlag, Berlin, 1990 | MR

[15] Hilbert D., Bernays P., Grundlagen der Mathematik, v. 2, Die Grundlehren d. math. Wiss. in Einzeldarstell. mit besonderer Berucksichtigung d. Anwendungsgebiete, 50, Julius Springer, Berlin, 1939 | Zbl

[16] Morozov A. S., “Funktsionalnye derevya i avtomorfizmy modelei”, Algebra i logika, 32:1 (1993), 54–72 | MR | Zbl

[17] Jockusch C. G. (jun.), Shore R. A., “Pseudo-jump operators. II. Transfinite iterations, hierarchies, and minimal covers”, J. Symb. Log., 49 (1984), 1209–1236 | MR

[18] Yates C. E. M., “On the degrees of index sets”, Trans. Am. Math. Soc., 121 (1966), 309–328 | MR | Zbl