2nd Semester 2020/21: The Algebra of Logic
- Nick Bezhanishvili and Tommaso Moraschini
What is the relation that connects logic and algebra? This project is a gentle introduction to the theory of algebraizable logics, a framework where a precise answer to this question can be given.
Motivated by the case of modal and intuitionistic logic, we will introduce a general theory of algebraization and use it investigate bridge theorems that connect metalogical properties (such as the deduction theorem) with their algebraic counterparts.
The project will be based on 12 previously recorded video lectures of 45 minutes each, complemented by detailed lecture notes. This material will be made available on the webpage of the teacher. Each week there will be digital office hours via Zoom, where further examples will be discussed. The communication with the teacher will happen via emails and Zoom.
Ideally, the participants should be familiar with the material of the course "Mathematical Structures in Logic". Basic knowledge of Priestley and Esakia dualities as well as of Universal Algebra will be useful.
At the end of the course, students will give a presentation and write a final report on topics related to the course. The assessment will be based on this work.
Lecture notes will be made available on the teacher's webpage. These will be selfcontained and should suffice as a reference for the course.