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 degree b.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Downey, R.: On Presentations of Algebraic Structures. In: Sorbi, A. (ed.) Complexity, Logic, and Recursion Theory, pp. 157–205 Dekker, New York (1997)
Ershov, Y.L.: On a hierarchy of sets II. Algebra i Logika 7(4), 15–47 (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 Logic 136, 219–246 (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 Logic 115, 71–113 (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 Logic 51, 1034–1042 (1986)
Miller, R.G.: The \(\Delta_2^0\)-spectrum of a linear order. Journal of Symbolic Logic 66, 470–486 (2001)
Morozov, A.S., Puzarenko, V.G.: Σ-Subsets of Natural Numbers. Algebra and Logic 43(3), 162–178 (2004)
Richter, L.J.: Degrees of Structures. Journal of Symbolic Logic 46, 723–731 (1981)
Slaman, T.: Relative to any Nonrecursive Set. Proceedings of the American Mathematical Society 126, 2117–2122 (1998)
Soskov, I.N.: Degree spectra and co-spectra of structures. Ann. Univ. Sofia 96, 45–68 (2003)
Wehner, S.: Enumerations, Countable Structures, and Turing Degrees. Proceedings of the American Mathematical Society 126, 2131–2139 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kalimullin, I. (2007). Some Notes on Degree Spectra of the Structures. In: Cooper, S.B., Löwe, 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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)