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)


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’.


Main Module Active Stage Successful Attack Expansionary Stage Recursion Theory 
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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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