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On Mass Problems of Presentability

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Theory and Applications of Models of Computation (TAMC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3959))

Abstract

We consider the notion of mass problem of presentability for countable structures, and study the relationship between Medvedev and Muchnik reducibilities on such problems and possible ways of syntactically characterizing these reducibilities. Also, we consider the notions of strong and weak presentability dimension and characterize classes of structures with presentability dimensions 1.

This work was supported by the INTAS YSF (grant 04-83-3310), the program ”Universities of Russia” (grant UR.04.01.488), the Russian Foundation for Basic Research (grant 05-01-00481a) and the Grant of the President of RF for Young Scientists (grant MK.1239.2005.1). Part of this work was done while the author was visiting the Department of Mathematics and Computer Science “Roberto Magari” of the University of Siena.

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References

  1. Barwise, J.: Admissible Sets and Strucrures. Springer, Berlin (1975)

    Google Scholar 

  2. Calvert, W., Cummins, D., Knight, J., Miller, S.: Comparing classes of finite structures. Algebra and Logic 43, 374–392 (2004)

    Article  MathSciNet  Google Scholar 

  3. Dyment, E.Z.: Certain properties of the Medvedev Lattice. Mat. Sbornik (NS). 101, 360–379 (1976)

    MathSciNet  Google Scholar 

  4. Ershov, Y.L.: Definability and Computability. Plenum, New York (1996)

    Google Scholar 

  5. Knight, J.F.: Degrees coded in jumps of orderings. J. Symbolic Logic 51, 1034–1042 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Knight, J.F.: Degrees of models. In: Handbook of Recursive Mathematics, vol. 1, pp. 289–309. Elsevier, Amsterdam (1998)

    Chapter  Google Scholar 

  7. Medvedev, Y.T.: Degrees of the mass problems. Dokl. Acad. Nauk SSSR (NS) 104, 501–504 (1955)

    MATH  Google Scholar 

  8. Miller, J.: Degrees of unsolvability of continuous functions. J. Symbolic Logic. 69, 555–584 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Muchnik, A.A.: On strong and weak reducibilities of algorithmic problems. Sibirsk. Mat. Zh. 4, 1328–1341 (1963)

    MATH  Google Scholar 

  10. Rozinas, M.: The semilattice of e-degrees. Recursive functions (Russian). Ivanov. Gos. Univ. Ivanovo, 71–84 (1978)

    Google Scholar 

  11. Selmam, A.: Arithmetical reducibilities. I. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 17, 335–350 (1971)

    Article  Google Scholar 

  12. Slaman, T.A.: Relative to any non-recursive set. Proc. Amer. Math. Soc. 126, 2117–2122 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sorbi, A.: The Medvedev lattice of degrees of difficulty. LMS Lecture Notes. Computability, Enumerability, Unsolvability: Directions in Recursion Theory 24, 289–312 (1996)

    Article  MathSciNet  Google Scholar 

  14. Soskov, I.N.: Degree spectra and co-spectra of structures. Ann. Univ. Sofia 96, 45–68 (2003)

    MathSciNet  Google Scholar 

  15. Stukachev, A.I.: On degrees of presentability of structures. I. Algebra and Logic (submitted)

    Google Scholar 

  16. Richter, L.: Degrees of structures. J. Symbolic Logic 46, 723–731 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wehner, S.: Enumerations, countable structures and Turing degrees. Proc. Amer. Math. Soc. 126, 2131–2139 (1998)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Alexey Stukachev

Authors
  1. Alexey Stukachev
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Editor information

Editors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 53706, Madison, WI, USA

    Jin-Yi Cai

  2. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  3. State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences,  

    Angsheng Li

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© 2006 Springer-Verlag Berlin Heidelberg

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Stukachev, A. (2006). On Mass Problems of Presentability. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_74

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  • DOI: https://doi.org/10.1007/11750321_74

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34021-8

  • Online ISBN: 978-3-540-34022-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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