# Introduction to algebraic logic

** Dr. Nicolò Zamperlin**Università degli Studi di Cagliari

**Abstract**

The course is an introduction to the theory of algebraizability of Blok and Pigozzi. Through an analytic study of the first chapters of Font’s handbook on abstract algebraic logic we will first introduce the elementary notions of universal algebra needed for linking together logic and algebra (closure operators and their lattices, varieties, quasivarieties and equational consequences), then building upon these notions we will consider the case of implicative logics and their algebraic properties, introducing the technique of completeness through the Lindenbaum-Tarski process. Finally we generalize these notions to the class of algebraizable logics (with a glimpse to the larger Leibniz heirarchy), with the ultimate goal of proving the isomorphism theorem and the transfer for the deduction theorem.

**Schedule**

The course will have a duration of 20 hours, scheduled as follows:

- November 7, aula B, h. 15-17
- November 14, aula A, h. 15-17
- November 22, aula II, h. 9:30-11:30
- November 29, aula II, h. 9:30-11:30
- December 2, aula II, h. 9:30-11
- December 6, aula II, h. 9:30-11:30
- December 12, aula B, h. 15-17
- January 15, aula B, h. 10-12
- January 20, aula B, h. 15-17
- February 3, aula B, h. 10-12

**Exam**

The final exam consists in a seminar presentation. The course will be held in person. Please contact me if you are interested in joining the course

**References**

- Bergman, C., Universal Algebra: Fundamentals and Selected Topics, Chapman & Hall Pure and Applied Mathematics, Chapman and Hall/CRC, 2011.
- Blok, W., and Pigozzi, D., Algebraizable logics, vol. 396 of Memoirs of the American Mathematical Society, A.M.S., 1989.
- Burris, S., and Sankappanavar, H.P., A course in Universal Algebra, freely available online: https://www.math.uwaterloo.ca/snburris/htdocs/ualg.html, 2012 update.
- Czelakowski, J., Protoalgebraic logics, vol. 10 of Trends in Logic: Studia Logica Library, Kluwer Academic Publishers, Dordrecht, 2001.
- Font, J.M., Abstract Algebraic Logic: An Introductory Textbook, College Publications, 2016