Abstract
In the paper the problem of existence of an algebraic structure with the degree spectra \(\{\bf x:\bf x\not\le\bf b\}\) is studied for arbitrary degreeĀ b.
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References
Downey, R.: On Presentations of Algebraic Structures. In: Sorbi, A. (ed.) Complexity, Logic, and Recursion Theory, pp. 157ā205 Dekker, New York (1997)
Ershov, Y.L.: On a hierarchy of sets II. Algebra i LogikaĀ 7(4), 15ā47 (1968)
Goncharov, S.S., Harizanov, V.S., Knight, J.F., McCoy, C., Miller, R., Solomon, R.: Enumerations in computable structure theory. Annals of Pure and Applied LogicĀ 136, 219ā246 (2005)
Hirschfeldt, D.R., Khoussainov, B., Shore, R.A., Slinko, A.M.: Degree spectra and computable dimensions in algebraic structures. Annals of Pure. and Applied LogicĀ 115, 71ā113 (2002)
Kalimullin, I.Sh.: Degree spectra of some algebraic structures, Algebra and Logic (to appear)
Kalimullin, I.Sh.: A non-\(\Delta_2^0\) structure is computable in any non-\(\Delta_2^0\) degree (to appear)
Kalimullin, I.Sh.: Restrictions on degree spectra of structures (to appear)
Knight, J.F.: Degrees coded in jumps of orderings. Journal of Symbolic LogicĀ 51, 1034ā1042 (1986)
Miller, R.G.: The \(\Delta_2^0\)-spectrum of a linear order. Journal of Symbolic LogicĀ 66, 470ā486 (2001)
Morozov, A.S., Puzarenko, V.G.: Ī£-Subsets of Natural Numbers. Algebra and LogicĀ 43(3), 162ā178 (2004)
Richter, L.J.: Degrees of Structures. Journal of Symbolic LogicĀ 46, 723ā731 (1981)
Slaman, T.: Relative to any Nonrecursive Set. Proceedings of the American Mathematical SocietyĀ 126, 2117ā2122 (1998)
Soskov, I.N.: Degree spectra and co-spectra of structures. Ann. Univ. SofiaĀ 96, 45ā68 (2003)
Wehner, S.: Enumerations, Countable Structures, and Turing Degrees. Proceedings of the American Mathematical SocietyĀ 126, 2131ā2139 (1998)
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Kalimullin, I. (2007). Some Notes on Degree Spectra of the Structures. In: Cooper, S.B., Lƶwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_40
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DOI: https://doi.org/10.1007/978-3-540-73001-9_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73000-2
Online ISBN: 978-3-540-73001-9
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