After successful completion of the course, students are able to distinguish first- and second order logic. They will be capable of formalizing and verifying mathematical theorems in systems of higher-order logic. The course will provide a deeper understanding of arithmetic theories and the theory of natural numbers, thus laying the foundation to scientific research.

• repetition of first-order logic and its main results
• second-order logic
• model theory of second-order logic
• second-order arithmetic and its properties
• proof theory of second-order arithmetic
• simple type theory
• higher-order logic
• model theory of higher-order logic
• the problem of completeness
• automated deduction in higher-order logic

presentation in lecture, exercises and discussion of solutions

Literature:

• G. Takeuti: Proof Theory, 2nd Edition, 1987, North Holland

oral examination and participation in exercises and discussions

Firm knowledge in first-order logic