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The Strongest Nonsplitting Theorem

  • Mariya Ivanova Soskova
  • S. Barry Cooper
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4484)

Abstract

Sacks [14] showed that every computably enumerable (c.e.) degree ≥ 0 has a c.e. splitting. Hence, relativising, every c.e. degree has a Δ 2 splitting above each proper predecessor (by ’splitting’ we understand ’nontrivial splitting’). Arslanov [1] showed that 0’ has a d.c.e. splitting above each c.e. a < 0’. On the other hand, Lachlan [9] proved the existence of a c.e. a > 0 which has no c.e. splitting above some proper c.e. predecessor, and Harrington [8] showed that one could take a = 0’. Splitting and nonsplitting techniques have had a number of consequences for definability and elementary equivalence in the degrees below 0’.

Keywords

Main Module Active Stage Successful Attack Expansionary Stage Recursion Theory 
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 2007

Authors and Affiliations

  • Mariya Ivanova Soskova
    • 1
  • S. Barry Cooper
    • 1
  1. 1.University of Leeds, Leeds, LS2 9JTUK

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