Three theorems on n-REA degrees: proof-readers and verifiers

  • Authors:

  • Mingzhong Cai

  • Affiliations:

  • Department of Mathematics, Cornell University, Ithaca, NY

  • Venue:
  • CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
  • Year:
  • 2011

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Abstract

We first show that an n-REA degree is array recursive if and only if it is r.e. traceable. This gives an alternate proof that an n-REA degree has a strong minimal cover if and only if it is array recursive. Then we prove that an n-REA degree is strongly jump traceable if and only if it is strongly superlow. These two results both generalize corresponding equivalence theorems for the r.e. degrees. In these proofs, we provide an interesting technique to handle n-REA degrees, which also gives a new proof of an old result that every FPF n-REA degree is complete.