Publication History of:

An Extension of the Recursively Enumerable Turing Degrees

Stephen G. Simpson

Professor of Mathematics

Pennsylvania State University

`http://www.personal.psu.edu/t20/`

July 20, 2006

An Extension of the Recursively Enumerable Turing Degrees

Stephen G. Simpson

Professor of Mathematics

Pennsylvania State University

July 20, 2006

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.

- Submitted August 10, 2004 for publication in Annals of
Mathematics. Rejection letter postmarked August 25, 2004, received
September 13, 2004.
- Submitted September 13, 2004 for publication in the American
Journal of Mathematics. Rejection letter postmarked September 28,
2004, received October 6, 2004.
- Submitted October 7, 2004 for publication in the Journal of the
American Mathematical Society. Rejection letter received November
16, 2004.
- 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 Withdrawn June 27, 2005.
- 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.
- Submitted August 22, 2005 for publication in the Journal of the
London Mathematical Society. Acceptance letter dated July 4, 2006,
received July 20, 2006.

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The translation was initiated by Stephen G Simpson on 2008-04-28

Stephen G Simpson 2008-04-28