Advanced course in foundations of mathematics (2015/2016)

Course code
Peter Michael Schuster
Academic sector
Language of instruction
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 1 3 II semestre Riccardo Bruni
Teoria 3 II semestre Peter Michael Schuster

Lesson timetable

II semestre
Activity Day Time Type Place Note
Teoria 1 Monday 2:30 PM - 4:30 PM lesson Laboratory Laboratorio Ciberfisico from May 9, 2016  to Jun 10, 2016
Teoria 1 Tuesday 8:30 AM - 11:30 AM lesson Lecture Hall M from May 10, 2016  to Jun 10, 2016
Teoria Tuesday 8:30 AM - 11:30 AM lesson Lecture Hall M from Mar 31, 2016  to May 3, 2016
Teoria Wednesday 10:30 AM - 12:30 PM lesson Lecture Hall M from Mar 31, 2016  to May 4, 2016

Learning outcomes

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.).

Assessment methods and criteria

Written or oral examination, depending on the number of candidates who want to sit the exam.

Reference books
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
Teoria Yiannis N. Moschovakis Notes on Set Theory Springer 1994 978-1-4757-4155-1