2nd Semester 2022/23: The Algebra of Logic
- Tommaso Moraschini (University of Barcelona) and Nick Bezhanishvili
- 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 the general theory of algebraization and use it to investigate bridge theorems that connect metalogical properties (such as the deduction theorem) with their algebraic counterparts.
- The project will be based on 6 lectures of 1.5 hours each complemented by detailed lecture notes. Each week there will be office hours, where doubts and questions can be resolved.
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.