Abstract
A relativized version of the notion of Degree spectrum of a structure with respect to finitely many abstract structures is presented, inspired by the notion of relatively intrinsic sets. The connection with the notion of Joint spectrum is studied. Some specific properties like Minimal Pair type theorem and the existence of Quasi-Minimal degree with respect to the Relative spectrum are shown.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ash, C.J.: Generalizations of enumeration reducibility using recursive infinitary propositional senetences. Ann. Pure Appl. Logic 58, 173–184 (1992)
Ash, C.J., Knight, J.F., Manasse, M., Slaman, T.: Generic copies of countable structures. Ann. Pure Appl. Logic 42, 195–205 (1989)
Ash, C.J., Jockush, C., Knight, J.F.: Jumps of orderings. Trans. Amer. Math. Soc. 319, 573–599 (1990)
Chisholm, J.: Effective model theory vs. recursive model theory. J. Symbolic Logic 55, 1168–1191 (1990)
Cooper, S.B.: Partial degrees and the density problem. Part 2: The enumeration degrees of the Σ2 sets are dense. J. Symbolic Logic 49, 503–513 (1984)
Downey, R.G., Knight, J.F.: Orderings with αth jump degree 0(α). Proc. Amer. Math. Soc. 114, 545–552 (1992)
Knight, J.F.: Degrees coded in jumps of orderings. J. Symbolic Logic 51, 1034–1042 (1986)
Richter, L.J.: Degrees of structures. J. Symbolic Logic 46, 723–731 (1981)
Soskov, I.N.: A jump inversion theorem for the enumeration jump. Arch. Math. Logic 39, 417–437 (2000)
Soskov, I.N.: Degree spectra and co-spectra of structures. Ann. Univ. Sofia 96, 45–68 (2004)
Soskov, I.N., Baleva, V.: Ash’s theorem for abstract structures. In: Proceedings of Logic Colloquium 2002 (to appear, 2002)
Soskova, A.A., Soskov, I.N.: Co-spectra of joint spectra of structures. Ann. Univ. Sofia 96, 35–44 (2004)
Soskova, A.A.: Minimal Pairs and Quasi-minimal degrees for the Joint Spectra of Structures. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds.) CiE 2005. LNCS, vol. 3526, pp. 451–460. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Soskova, A.A. (2006). Relativized Degree Spectra. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_56
Download citation
DOI: https://doi.org/10.1007/11780342_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35466-6
Online ISBN: 978-3-540-35468-0
eBook Packages: Computer ScienceComputer Science (R0)