Archive for Mathematical Logic

, Volume 29, Issue 3, pp 201–211 | Cite as

Working below a low2 recursively enumerably degree

  • Richard A. Shore
  • Theodore A. Slaman


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  1. Fejer, P.A., Shore, R.A.: Embeddings and extension of embeddings in the r.e. tt- and wtt-degrees. In: Ebbinghaus, H.D. et al. (eds.) Recursion theory week. Berlin: Springer 1985 (Lect. Notes Math., vol. 1141), pp. 121–140)Google Scholar
  2. Harrington L., Slaman, T.: An interpretation of arithmetic in the theory of the furing degrees of the recursively enumerable sets. (1990, in preparation)Google Scholar
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  5. Lerman, M.: Degrees of unsolvability. Berlin: Springer, 1983Google Scholar
  6. Robinson, R.W.: Interpolation and embedding in the recursively enumerable degrees. Ann. Math. II. Ser.93, 586–596 (1971)Google Scholar
  7. Shore, R.A.: On the ∀∃-sentences of α-recursion theory. In: Fenstad, J.E., Gandy, R.O., Sacks, G.E. (eds.) Generalized recursion theory II. Amsterdam: North-Holland, pp. 331–354, 1978Google Scholar
  8. Shore, R.A.: Defining jump classes in the degrees below 0. Proc. Am. Math. Soc.104, 287–292 (1988)Google Scholar
  9. Shore, R.A., Slaman, T.: Working below a high recursively enumerable degree (1990)Google Scholar
  10. Shore, R.A., Slaman, T.: Splitting and density cannot be combined below any high r.e. degree (1991)Google Scholar
  11. Soare, R.I.: Recursively enumerable sets and degrees. Berlin: Springer, 1987Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Richard A. Shore
    • 1
  • Theodore A. Slaman
    • 2
  1. 1.Department of MathematicsCornell UniversityIthacaUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA
  3. 3.Mathematical Science Research InstituteBerkeleyUSA

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