Abstract
We present a notion of a degree spectrum of a structure with respect to countably many sets, based on the notion of ω-enumeration reducibility. We prove that some properties of the degree spectrum such as the minimal pair theorem and the existence of quasi-minimal degree are true for the ω-degree spectrum.
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References
Ash, C.J.: Generalizations of enumeration reducibility using recursive infinitary propositional senetences. Ann. Pure Appl. Logic 58, 173–184 (1992)
Cooper, S.B.: Partial degrees and the density problem. Part 2: The enumeration degrees of the Σ2 sets are dense. J. Symb. Logic 49, 503–513 (1984)
Cooper, S.B.: Computability Theory. Chapman & Hall/CRC, Boca Raton (2004)
Ganchev, H.: A jump inversion theorem for the infinite enumeration jump. Ann. Sofia Univ ( to appear, 2005)
Ganchev, H.: Exact Pair Theorem for the ω-Enumeration Degrees. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds.) CiE 2007. LNCS, vol. 4497, pp. 316–324. Springer, Heidelberg (2007)
Richter, L.J.: Degrees of structures. J. Symb. 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. Sofia Univ. 96, 45–68 (2004)
Soskov, I.N., Baleva, V.: Ash’s theorem for abstract structures. In: Chatzidakis, Z., Koepke, P., Pohlers, W. (eds.) Proc. of Logic Colloquium 2002, Muenster, Germany, 2002. Lect. Notes in Logic, vol. 27, pp. 327–341. ASL (2006)
Soskov, I.N., Kovachev, B.: Uniform regular enumerations. Mathematical Structures in Comp. Sci. 16(5), 901–924 (2006)
Soskov, I.N.: The ω-enumeration degrees. J. Logic and Computation 17(6), 1193–1214 (2007)
Soskov, I.N., Ganchev, H.: The jump operator on the ω-enumeration degrees. Ann. Pure Appl. Logic (to appear)
Soskova, A.A.: Relativized degree spectra. J. Logic and Computation 17(6), 1215–1233 (2007)
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Soskova, A.A. (2008). ω-Degree Spectra. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_58
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DOI: https://doi.org/10.1007/978-3-540-69407-6_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69405-2
Online ISBN: 978-3-540-69407-6
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