Summary
We state and prove the Translation Theorem. Then we apply the Translation Theorem to Soare's Extension Theorem, weakening slightly the hypothesis to yield a theorem we call the Modified Extension Theorem. We use this theorem to reprove several of the known results about orbits in the lattice of recursively enumerable sets. It is hoped that these proofs are easier to understand than the old proofs.
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Mathematics subject classification (1991): 03D25
The author was partially supported by a NSF Postdoctoral Fellowship and by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University and wishes to thank Michael Stob and Rodney Downey for their help
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Cholak, P. The translation theorem. Arch Math Logic 33, 87–108 (1994). https://doi.org/10.1007/BF01352931
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DOI: https://doi.org/10.1007/BF01352931