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Partial functions and domination

C.T. Chong, Gordon Hoi, Frank Stephan, Daniel Turetsky, S. Barry Cooper
2015 Logical Methods in Computer Science  
While there is a full π01-class of nonrecursive sets where no set is pdominant, there is no π01-class containing only pdominant sets.  ...  No set which is low for Martin-Löf random is pdominant. There is a low r.e. set which is pdominant and a high r.e. set which is not pdominant.  ...  Acknowledgments The authors want to thank Noam Greenberg for discussions and correspondence on this subject; furthermore they are greatful to the anonymous referees for detailed and comprehensive comments  ... 
doi:10.2168/lmcs-11(3:16)2015 fatcat:j2ajshjp7fh4fbmaa7zfdwurhi