Computability and Logic

Lecturer: Prof. Dr. Heribert Vollmer

Frequency: Every two years (odd-numbered years) in the summer semester

Course Type: Lecture, exercise, and seminar (2V + 1Ü + 2S, 7 ECTS)

Examination: Oral exam

This course provides in-depth knowledge about the challenges of computability and provability. After successful completion, students understand the significance of mathematical logic in computer science. They gain an understanding of the possibilities and limits of computability, formalizability, and provability. They analyze computational problems with respect to their formalizability and solvability.

Content:

This lecture addresses the question of which computational problems can be solved algorithmically at all. Starting from the undecidability of the so-called Halting Problem, we will explore various levels of algorithmic unsolvability. Particularly interesting insights arise in the field of mathematical logic; here we will focus especially on Gödel's incompleteness theorems.

Outline:

• Recursively enumerable sets
• First-order predicate logic
• Undecidability of first-order predicate logic
• Proofs in first-order predicate logic
• Arithmetical definability
• Representability
• Gödel’s incompleteness theorem
• The arithmetical hierarchy
• Relative computability