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Archive for Mathematical Logic

, Volume 36, Issue 4–5, pp 255–267 | Cite as

Definability in the enumeration degrees

  • Theodore A. Slaman
  • W. Hugh Woodin

Abstract.

We prove that every countable relation on the enumeration degrees, \({\frak E}\), is uniformly definable from parameters in \({\frak E}\). Consequently, the first order theory of \({\frak E}\) is recursively isomorphic to the second order theory of arithmetic. By an effective version of coding lemma, we show that the first order theory of the enumeration degrees of the \(\Sigma^0_2\) sets is not decidable.

Keywords

Order Theory Effective Version Countable Relation Enumeration Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Theodore A. Slaman
    • 1
  • W. Hugh Woodin
    • 1
  1. 1. Department of Mathematics, University of Chicago, Chicago, IL 60637, USA US

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