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The impossibility of finding relative complements for recursively enumerable degrees

A. H. Lachlan

Journal of Symbolic Logic 31 (3):434-454 (1966)

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Parameter definability in the recursively enumerable degrees.André Nies - 2003 - Journal of Mathematical Logic 3 (01):37-65.details The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the [Formula: see text] relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k ≥ 7, the [Formula: see text] relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that Low 1 is parameter definable, and we provide methods that lead to a new example of a ∅-definable ideal. Moreover, we prove that (...) Download Export citation Bookmark 6 citations
The weak truth table degrees of recursively enumerable sets.Richard E. Ladner & Leonard P. Sasso - 1975 - Annals of Mathematical Logic 8 (4):429-448.details Download Export citation Bookmark 33 citations
Conjectures and questions from Gerald Sacks's Degrees of Unsolvability.Richard A. Shore - 1997 - Archive for Mathematical Logic 36 (4-5):233-253.details We describe the important role that the conjectures and questions posed at the end of the two editions of Gerald Sacks's Degrees of Unsolvability have had in the development of recursion theory over the past thirty years. Download Export citation Bookmark 2 citations
Definability in the recursively enumerable degrees.André Nies, Richard A. Shore & Theodore A. Slaman - 1996 - Bulletin of Symbolic Logic 2 (4):392-404.details §1. Introduction. Natural sets that can be enumerated by a computable function always seem to be either actually computable or of the same complexity as the Halting Problem, the complete r.e. set K. The obvious question, first posed in Post [1944] and since then called Post's Problem is then just whether there are r.e. sets which are neither computable nor complete, i.e., neither recursive nor of the same Turing degree as K?Let be the r.e. degrees, i.e., the r.e. sets modulo (...) Download Export citation Bookmark 4 citations
Degree structures: Local and global investigations.Richard A. Shore - 2006 - Bulletin of Symbolic Logic 12 (3):369-389.details The occasion of a retiring presidential address seems like a time to look back, take stock and perhaps look ahead.Institutionally, it was an honor to serve as President of the Association and I want to thank my teachers and predecessors for guidance and advice and my fellow officers and our publisher for their work and support. To all of the members who answered my calls to chair or serve on this or that committee, I offer my thanks as well. Your (...) Download Export citation Bookmark 4 citations

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