Recommended References on Computability Theory

These are some selected references in .pdf form for graduate students in connection with the Logic Seminar and Soare's course on computability theory.

General Computable Model Theory

Valentina Harizanov Handbook article on computable model theory.
Harizanov handbook.pdf

Computable Content of Vaught's Models

For Soare's Leeds turorial (prerequisites and beginning exposition) and out line of four lectures) see
Robert Soare, Computable Content of Vaught's Models, four lectures, August 21-25, MATHLOGAPS, University of Leeds, U.K.

Computability of Prime, Saturated, and Homogeneous Models

For recent results on computable content of Vaught's models (prime models, saturated models, homogeneous models) see the following:

Barbara F. Csima
Degree spectra of prime models J. Symbolic Logic, vol. 69 (2004), pp. 430--442. (pdf file)

Barbara Csima, Denis Hirschfeldt, Julia Knight, Robert Soare,
Bounding Prime Models J. Symbolic Logic, vol. 69 (2004), pp. 1117-1142. (pdf file)

Barbara F. Csima, Valentina S. Harizanov, Denis R. Hirschfeldt, and Robert I. Soare,
Bounding Homogeneous Models J. Symbolic Logic, to appear. (pdf)

Karen Lange and Robert I. Soare,
Computable Content of Homogeneous Models J. Symbolic Logic, to appear. (pdf)

Computable Content of Boolean Algebras

Carl Jockusch, Robert Soare, Boolean algebras, Stone spaces, and the iterated Turing jump, J. of Symbolic Logic , 59 (1994) 1121--1138.
Boolean.pdf .

Differential Geometry

For applications of computablity to differential geometry and applications of identity bounded Turing reducibility (ibT) see the paper by Soare Computability Theory and Differential Geometry which appeared in the Bull. ASL in Dec, 2004.

The computability theoretic results for the differential geometry appear in a joint paper:
Barbara Csima and Robert Soare, Computability Results Used in Differential Geometry, J. Symbolic Logic, to appear.

Nabutovsky-Weinberger on Diffential Geometry

For the Nabutovsky and Weinberger papers.pdf on differential geometry see:

[NW1, 2000]
A.~Nabutovsky and S.~Weinberger, Variational problems for Riemannian functionals and arithmetic groups, Publications Math\'ematiques, Institut des Hautes \'Etudes Scientifiques, no. 92, (2000), 5--62. NabW1.pdf

[NW2, 2003]
A. Nabutovsky and S. Weinberger, The Fractal Nature of Riem/Diff I, Geometrica Dedicata 101 (2003), 1-54. NabW2.pdf

Downey Hirschfeldt Book on Effective Randomness and Kolmogorov Complexity

There are additional references and readings on computability theory assigned from the Downey Hirschfeldt book, "Algorithmic Randomness and Complexity," Downey-Hirschfeldt maindoc.pdf

History and Philosophy of Computability Theory

Related and recommended papers on the history and philosophy of computabilty include W. Sieg, "G\"odel on computability," sieg.pdf

Robert I. Soare, Computability and Recursion Bull ASL, 1996 A history of computability and recursion, the role they play in the subject, Soare compute.pdf