Splitting Theorems and the Jump Operator

  title={Splitting Theorems and the Jump Operator},
  author={Rodney G. Downey and Richard A. Shore},
  journal={Ann. Pure Appl. Logic},
We investigate the relationship of (jumps of) the degrees of splittings of a computably enumerable set and the degree of the set. We prove that there is a high computably enumerable set whose only proper splittings are low2. ∗Research partially supported by the U.S. ARO through ACSyAM at the Mathematical Sciences Institute of Cornell University Contract DAAL03-91-C-0027, the IGC of Victoria University and the Marsden Fund for Basic Science under grant VIC-509. §Research partially supported by… CONTINUE READING

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