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On Differences Among Elementary Theories of Finite Levels of Ershov Hierarchies

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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 study the differences among elementary theories of finite levels of Ershov hierarchies. We also give a brief survey on the current state of this area. Some questions are raised.

Both authors were partially supported by NUS Grant No. R-146-000-078-112 (Singapore). The second author is supported by postdoctoral fellowship from NUS, NSF of China No. 10471060 and No. 10420130638.

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References

  1. Ambos-Spies, K., Jockusch Jr., C.G., Shore, R.A., Soare, R.I.: An algebraic decomposition of the recursively enumerable degrees and the coincidence of several degree classes with the promptly simple degrees. Trans. Amer. Math. Soc. 281(1), 109–128 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arslanov, M.M.: Lattice properties of the degrees below O’. Dokl. Akad. Nauk SSSR 283(2), 270–273 (1985)

    MathSciNet  Google Scholar 

  3. Arslanov, M.M., Kailimulin, I., Lempp, S.: On downey’s conjecture (to appear)

    Google Scholar 

  4. Cholak, P., Groszek, M., Slaman, T.: An almost deep degree. J. Symbolic Logic 66(2), 881–901 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Barry Cooper, S., Harrington, L., Lachlan, A.H., Lempp, S., Soare, R.I.: The d.r.e. degrees are not dense. Ann. Pure Appl. Logic 55(2), 125–151 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Downey, R.: D.r.e. degrees and the nondiamond theorem. Bull. London Math. Soc. 21(1), 43–50 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hodges, W.: Model theory. Encyclopedia of Mathematics and its Applications, vol. 42. Cambridge University Press, Cambridge (1993)

    Book  MATH  Google Scholar 

  8. Nies, A.: Parameter definability in the recursively enumerable degrees. J. Math. Log. 3(1), 37–65 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Putnam, H.: Trial and error predicates and the solution to a problem of Mostowski. J. Symbolic Logic 30, 49–57 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sacks, G.E.: Sacks. A minimal degree less than 0’. Bull. Amer. Math. Soc. 67, 416–419 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  11. Sacks, G.E.: The recursively enumerable degrees are dense. Ann. of Math. 80(2), 300–312 (1964)

    Article  MathSciNet  Google Scholar 

  12. Shore, R.A., Slaman, T.A.: Working below a high recursively enumerable degree. J. Symbolic Logic 58(3), 824–859 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  13. Soare, R.I.: Recursively enumerable sets and degrees. Springer, Berlin (1987)

    Google Scholar 

  14. Wang, W., Yu, L.: Realizing Σ1 formulas in R (unpublished notes)

    Google Scholar 

  15. Yang, Y., Yu, L.: On Σ1-structural differences among finite levels of Ershov hierarchies (to appear)

    Google Scholar 

  16. Yu, L., Yang, Y.: On the definable ideal generated by nonbounding c.e. degrees. J. Symbolic Logic 70(1), 252–270 (2005)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, 117543, Singapore

    Yue Yang & Liang Yu

Authors
  1. Yue Yang
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  2. Liang Yu
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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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Yang, Y., Yu, L. (2006). On Differences Among Elementary Theories of Finite Levels of Ershov Hierarchies. 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_73

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  • DOI: https://doi.org/10.1007/11750321_73

  • 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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