Publication History of:

An Extension of the Recursively Enumerable Turing Degrees

Stephen G. Simpson Professor of Mathematics Pennsylvania State University

               http://www.math.psu.edu/simpson/

July 20, 2006

My paper An extension of the recursively enumerable Turing degrees^{1} (15 pages, August 2004) includes some remarks on the lack of natural examples of recursively enumerable Turing degrees. See also my detailed remarks^{2} of February 2005. Although the facts of the matter are well known and indisputable, they have been strenuously disputed^{3} by Dr. Robert I. Soare^{4}, 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^{5} 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.

1. Submitted August 10, 2004 for publication in Annals of Mathematics. Rejection letter postmarked August 25, 2004, received September 13, 2. Submitted September 13, 2004 for publication in the American Jour-

1http://www.math.psu.edu/simpson/papers/extre.pdf

2http://www.cs.nyu.edu/pipermail/fom/2005-February/008809.html

3http://www.cs.nyu.edu/pipermail/fom/1999-August/003289.html

4http://people.cs.uchicago.edu/˜ soare/

5http://www.math.psu.edu/simpson/papers/compute.pdf

nal of Mathematics. Rejection letter postmarked September 28, 2004, received October 6, 2004.

3. Submitted October 7, 2004 for publication in the Journal of the American Mathematical Society. Rejection letter received November 16, 2004.

4. Submitted November 17, 2004 to a member of the U.S. National Academy of Sciences, for communication to the Proceedings of the National Academy of Sciences. After a positive but non-committal reply the same day, there was no further reply, despite repeated inquiries. Withdrawn June 27, 2005.

5. Submitted June 27, 2005 for publication in the Mathematical Proceedings of the Cambridge Philosophical Society. Rejection letter dated July 12, 2005, received approximately August 15, 2005.

6. Submitted August 22, 2005 for publication in the Journal of the London Mathematical Society. Acceptance letter dated July 4, 2006, received July 20, 2006.