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Online Research Papers (Publications)
Computable Content of Vaughtian Models
Robert Soare gave four lectures during August 21-25, 2006 at
MATHLOGAPS in Leeds on the topic of
Computable Content of Vaughtian Models,
a topic of current research interest at Chicago and elsewhere.
First Soare gave a
Tutorial on Vaught's Results
for graduate students in mathematical logic. No previous background
is necessary. Next are attached the transparencies of the four
lectures which examined the computable content of these models.
Lecture 1: Degrees of Prime Models
Lecture 2: Degrees Bounding Prime Models
Lecture 3: Degrees of Saturated Models
Lecture 4: Degrees of Homogeneous Models
Soare's 1987 book published by Springer-Verlag
has been widely used as a text and reference in computability
theory. He is now writing a new book
Computability Theory and Applications abbreviated [CTA]
under contract with Springer-Verlag.
This will have a lot more material on computability than
the old book and will have a number of chapters on applications
of computability to other areas.
Other Areas of Soare's Research
Computability and Differential Geometry
A paper by Soare,
Computability Theory and Differential Geometry has appeared in
the Bulletin of Symbolic Logic in December, 2004, about
applications of computability theory to differential geometry, See the
paper in .ps and .pdf form and see comments from the referee's
report.
Barbara Csima and Soare are completing their paper,
Computability Results Used in Differential Geometry, which
contains proofs of all the computability results used in the
differential geometry results mentioned here.
Other Items of Interest in Computability Theory:
The History and Concept of Computability.pdf , an expository,
nontechnical paper dealing
with the development of Turing computability and recursive functions,
published in the Bulletin of Symbolic Logic, 1996.