T-degrees, jump classes, and strong reducibilities

@inproceedings{Downey1987TdegreesJC,
  title={T-degrees, jump classes, and strong reducibilities},
  author={Rodney G. Downey and Carl G. Jockusch},
  year={1987}
}
It is shown that there exist r.e. degrees other than 0 and 0' which have a greatest r.e. 1-degree. This solves an old question of Rogers and Jockusch. We call such degrees 1-topped. We show that there exist incomplete 1-topped degrees above any low r.e. degree, but also show that no nonzero low degree is 1-topped. It then follows by known results that all incomplete 1-topped degrees are low2 but not low. We also construct cappable nonzero 1-topped r.e. degrees and examine the relationships… CONTINUE READING

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