The studente is required to know basic notions of set theory, algebra and topology.
The course aims at introducing some advanced topics in mathematical logic. The student will be asked to apply herself/himself with rigour in learning notions and proofs, and at the same time to develop a critical feeling about the role of logic in mathematics and in science in general.
Model Theory. The incompleteness theorems. Introduction to the theory of computability.
1) Classnotes distributed by the teacher.
2) R. Soare, Recursively Enumerable Sets and Degrees, Springer
3) B. Robic, The Foundations of Computability Theory, Springer
Lectures, with some workout sessions.
Final oral examination, with both theoretical questions (concerning definitions, theorems, and proofs) and practical questions (exrcises). No interim examination is scheduled.