Instructor: Joseph Zielinski
Office: Wean Hall 7101
Office hours: TBA
Class times: MWF 2:30pm-3:20pm
Class location: Baker Hall 136E
The course builds on the proof theory and model theory of first-order logic covered in 21-300. These are applied in 21-400 to Peano Arithmetic and its standard model, the natural numbers. The main results are the incompleteness, undefinability and undecidability theorems of Godel, Tarski, Church and others. Leading up to these, it is explained how logic is formalized within arithmetic, how this leads to the phenomenon of self-reference, and what it means for the axioms of a theory to be computably enumerable. Related aspects of computability theory are included to the extent that time permits.
The material covered in this course will be broken into several topics, all more-or-less independent from one another. The first topic is Gödel's incompleteness theorem. This will be developed in its entirety--presupposing only the material from 21-300--from the definition of a recursive function through the incompleteness theorem and related results. The later topics will be selected with the aim that they be interesting and accessible (at least as an introduction) to undergraduates who have taken basic logic, relevant to current mathematical research, but not necessarily covered in any of the other logic courses offered by the department.
Students' overall performance will be evaluated by the instructor. There will be periodic homework assignments given. The final course grade will be based on the homework scores and on attendance and participation.
Students are encouraged to work with one another on the homework problems, and are free to consult other textbooks to further their understanding of the material. However, the work that is submitted for credit must be completed by the student alone.
This syllabus is subject to change. Please consult this webpage regularly for the most current version.