[FOM] Intermediate Turing Degrees
Stephen G Simpson
simpson at math.psu.edu
Tue Aug 31 11:30:56 EDT 2010
Merlin Carl writes:
it is well known that there's a rich structure of Turing degrees
between 0 and 0`. However, [...] I have yet neither seen
intermediate degrees occuring in other disciplines of mathematics
nor corresponding to an application. [...]
Some years ago I was a principal participant in an extensive FOM
discussion of the role of intermediate r. e. Turing degrees and
priority arguments in what was then being called "applied
computability theory". See for instance:
http://cs.nyu.edu/pipermail/fom/1999-August/003299.html
http://www.cs.nyu.edu/pipermail/fom/1999-August/003327.html
http://www.cs.nyu.edu/pipermail/fom/1999-August/003331.html
http://www.cs.nyu.edu/pipermail/fom/2005-February/008809.html
Unfortunately, although the discussion was interesting and promising
from a scientific viewpoint, it became impossible to continue on the
FOM list. Instead I have continued the discussion in another way, by
publishing several relevant research articles:
Mass problems and randomness (BSL, 2005)
An extension of the recursively enumerable Turing degrees (JLMS, 2007)
Mass problems and almost everywhere domination (MLQ, 2007)
Some fundamental issues concerning degrees of unsolvability (CPOI II, 2008)
Mass problems and hyperarithmeticity (JML, 2008)
Mass problems and intuitionism (NDJFL, 2008)
Mass problems and measure-theoretic regularity (BSL, 2009)
All of these articles are available on my web page.
----
Name: Stephen G. Simpson
Affiliation: Pennsylvania State University
Research interests: foundations of mathematics, mathematical logic
Web page: http://www.math.psu.edu/simpson/
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