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Cupping the Recursively Enumerable Degrees by D.R.E. Degrees
Author(s) -
Li Angsheng,
Yi Xiaoding
Publication year - 1999
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611599011818
Subject(s) - recursively enumerable language , mathematics , turing , recursively enumerable set , maximal set , degree (music) , discrete mathematics , combinatorics , computer science , set (abstract data type) , physics , acoustics , programming language
We prove that there are two incomplete d.r.e. degrees (the Turing degrees of differences of two recursively enumerable sets) such that every non‐zero recursively enumerable degree cups at least one of them to 0 ′, the greatest recursively enumerable (Turing) degree. 1991 Mathematics Subject Classification : primary 03D25, 03D30; secondary 03D35.