116b- Syllabus

Math 116 provides an introduction to the basic concepts and results of mathematical logic and set theory. Math 116B will be devoted to computability theory and the incompleteness theorems.

(Additional topics may include the behavior of countable models and Hilbert’s 10th problem.)

Our approach to incompleteness will be somewhat non-standard and will allow us to discuss subsystems of second-order arithmetic.

Grading Policy: The grade for this course will be based on homework assignments. There will be no exams.

Solutions to homework problems should be written individually, although collaboration is allowed. All references used to solve a problem should be explicitly mentioned, including those students you collaborated with. You cannot look up solutions from any source.

No late submissions of solutions are allowed, except for medical problems (note needed from the health center) or serious personal difficulties (note needed from the Dean’s office).

Please try to solve as many problems as it seems reasonable from each set. Let me know if you find some problems to be too hard or too easy or to contain mistakes. Feedback is greatly appreciated.

Textbook: There is no required textbook. The following suggested references may be useful:

R. Cori and D. Lascar. Mathematical logic. A course with Exercises (Part II), OUP, 2001, ISBN 0198500505

T. Franzén. Inexhaustibility, ASL (A K Peters), ISBN 0198500505 J. Shoenfield. Mathematical logic, ASL (A K Peters), ISBN 1568811352S. Simpson. Subsystems of second order arithmetic, Springer, ISBN 3540648828

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