Mathematical logic (2020/2021)

Course code
Name of lecturer
Peter Michael Schuster
Peter Michael Schuster
Number of ECTS credits allocated
Academic sector
Language of instruction
I semestre dal Oct 1, 2020 al Jan 29, 2021.

Lesson timetable

Go to lesson schedule

Learning outcomes

The course is intended to introduce into the interaction between syntax (formal languages and calculi) and semantics (interpretations and models) as is fundamental for abstract mathematics and theoretical informatics.


With the exception of some optional exercise classes, the entire course will be held in lecture hall. At the same time all hours will be available online.

Contents of the course:

Formal languages of first-order predicate logic.
Calculus of natural deduction.
Minimal, intuitionistic and classical logic.
Soundness and completeness theorems.
Compactness and Löwenheim-Skolem theorems.
Models and theories.

Reference books
Author Title Publisher Year ISBN Note
Troelstra, Anne S. & Schwichtenberg, Helmut Basic Proof Theory. (Edizione 2) Cambridge University Press 2000 0-521-77911-1
Jon Barwise (ed.) Handbook of Mathematical Logic North-Holland 1977 0-444-86388-5
David, René & Nour, Karim & Raffali, Christophe Introduction à la Logique. Théorie de la démonstration (Edizione 2) Dunod 2004 9782100067961
Cantini, Andrea & Minari, Pierluigi Introduzione alla logica : linguaggio, significato, argomentazione. (Edizione 1) Le Monnier 2009 978-88-00-86098-7
van Dalen, Dirk Logic and Structure. (Edizione 5) Springer 2013 978-1-4471-4557-8
Abrusci, Vito Michele & Tortora de Falco, Lorenzo Logica. Volume 1 - Dimostrazioni e modelli al primo ordine. (Edizione 1) Springer 2015 978-88-470-5537-7
Shoenfield, Joseph R. Mathematical Logic. (Edizione 2) Association for Symbolic Logic & A K Peters 2001 1-56881-135-7
Schwichtenberg, Helmut Mathematical Logic (lecture notes). 2012
Helmut Schwichtenberg, Stanley S. Wainer Proofs and Computation Cambridge University Press 2012 9780521517690

Assessment methods and criteria

Single oral exam with open questions and grades out of 30. The exam modalities are equal for attending and non-attending students.

The exam's objective is to verify the full maturity about proof techniques and the ability to read and comprehend advanced arguments of mathematical logic.

The assessment methods may be subject to change as the development of the situation demands. La modalità a distanza è comunque garantita per tutti gli studenti che lo chiederanno nell’anno accademico 2020/21.