My paper An extension of the recursively enumerable Turing degrees (15 pages, August 2004) includes some remarks on the lack of natural examples of recursively enumerable Turing degrees. See also my detailed remarks of February 2005. Although the facts of the matter are well known and indisputable, they have been strenuously disputed by Dr. Robert I. Soare, Distinguished Service Professor of Mathematics and Computer Science at the University of Chicago.
Dr. Soare is a leading expert on the subject of recursively enumerable Turing degrees. See for example Dr. Soare's monograph Recursively Enumerable Sets and Degrees, Springer-Verlag, 1987. Furthermore, Dr. Soare is extraordinarily influential. For example, in the 1990's Dr. Soare demanded a wholesale revision of all of the terminology in recursion theory, one of the four major branches of mathematical logic. It is noteworthy that almost all of Dr. Soare's numerous followers have adopted his revised terminology.
Because of Dr. Soare's influence, I have encountered considerable difficulty in publishing my paper An extension of the recursively enumerable Turing degrees in an appropriate scholarly venue. The paper was originally submitted for publication on August 10, 2004. After nearly two years in limbo, the paper was finally accepted on July 4, 2006. Here is the publication history.
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