| Activity | Credits | Period | Academic staff | Timetable |
|---|---|---|---|---|
| Teoria 1 | 3 | II semestre | Riccardo Bruni | |
| Teoria | 3 | II semestre | Peter Michael Schuster |
The aim of the course is to provide the student with a more profound knowledge of the foundations of mathematics, from a mathematical perspective.
Introduction to Zermelo-Fraenkel style axiomatic set theory, with attention to constructive aspects and transfinite methods (ordinal numbers, axiom of choice, etc.).
Gödel's incompleteness theorems and their repercussion on Hilbert's programme, with elements of computability theory (recursive functions and predicates, etc.).
Written or oral examination, depending on the number of candidates who want to sit the exam.
| Activity | Author | Title | Publisher | Year | ISBN | Note |
| Teoria | Torkel Franzén | Gödel's Theorem: An Incomplete Guide to its Use and Abuse. | A K Peters, Ltd. | 2005 | 1-56881-238-8 | |
| Teoria | Jon Barwise (ed.) | Handbook of Mathematical Logic | North-Holland | 1977 | 0-444-86388-5 | Mainly the chapter "The incompleteness theorems" by Craig Smorynski. |
| Teoria | Riccardo Bruni | Kurt Gödel, un profilo. | Carocci | 2015 | 9788843075133 | |
| Teoria | Peter Aczel, Michael Rathjen | Notes on Constructive Set Theory | 2010 | http://www1.maths.leeds.ac.uk/~rathjen/book.pdf | ||
| Teoria | Yiannis N. Moschovakis | Notes on Set Theory | Springer | 1994 | 978-1-4757-4155-1 |
