Algebraic and Categorical Logic

The aim of the course is to introduce some of the basic and more advanced tools of the algebraic and categorical approaches to propositional and first-order logics, both classical and non-classical.

Upon completion of the course, students will possess in-depth knowledge of algebraic logic, including

- basic theory of algebraic and ordered structures
- Lindenbaum-Tarski construction
- representation theory and completeness results
- translation of logical-algebraic properties

and categorical logic, including

- syntactic categories and completeness results
- Grothendieck toposes and classifier toposes
- localic toposes and Deligne's theorem
- internal logic