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This article is cited in 4 scientific papers (total in 4 papers)
Simple structures with complex symmetry
V. Harizanova, R. Millerbc, A. S. Morozovd
a Dep. Math., George Washington Univ.,Washington, DC, USA
b Ph.D. Prog. Math. and Comp. Sci., C.U.N.Y. Graduate Center, New York, USA
c Dep. Math. Queens College – C.U.N.Y., New York, USA
d Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Abstract:
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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English version:
Algebra and Logic, 2010, 49:1, 68–90
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UDC:
510.5+510.67
Received: 14.09.2009
Citation:
V. Harizanov, R. Miller, A. S. Morozov, “Simple structures with complex symmetry”, Algebra Logika, 49:1 (2010), 98–134; Algebra and Logic, 49:1 (2010), 68–90
Citation in format AMSBIB
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\pages 68--90
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http://mi.mathnet.ru/eng/al430 http://mi.mathnet.ru/eng/al/v49/i1/p98
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Fokina E.B., Harizanov V., Melnikov A., “Computable Model Theory”, Turing'S Legacy: Developments From Turing'S Ideas in Logic, Lecture Notes in Logic, 42, ed. Downey R., Cambridge Univ Press, 2014, 124–194
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N. T. Kogabaev, “The theory of projective planes is complete with respect to degree spectra and effective dimensions”, Algebra and Logic, 54:5 (2015), 387–407
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N. Kh. Kasymov, A. S. Morozov, “Definability of linear orders over negative equivalences”, Algebra and Logic, 55:1 (2016), 24–37
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Miller R., Poonen B., Schoutens H., Shlapentokh A., “A Computable Functor From Graphs to Fields”, J. Symb. Log., 83:1 (2018), 326–348
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