An introduction to mathematical logic (continued)
10-09-04 (Institute Colloquium)
The second and third lectures in the series "Introduction to Logic" will be held on Friday, 10 September, from 2:00-5:00, with a break. Both these lectures will be taken by Adrien Deloro (ENS Lyon).
These two lectures will be a first step into Model Theory. Model Theory emphasises the importance of the language of first order logic in the study of a mathematical structure. We shall define and investigate some basic "first order notions" like elementary substructures or completeness. We shall also state the famous compactness theorem, and give some applications and examples in several mathematical fields.
Note: The final two lectures in this five lecture will be by Alexis Saurin on Proof Theory. The dates for these lectures will be annnounced later.
The last two lectures will be less concerned with the notion of truth than with the notion of provability. We shall introduce several ways to study mathematically the proofs done in mathematics (Natural Deduction, Sequent Calculus), and we will discuss the properties of these "formal proofs" considered as a mathematical objects like an integer or a function (and address such questions as: is it always possible to avoid the use of a lemma?). Furthermore, we will explain how proof theory relates with computer science and in what sense we can assert that proving is computing.