Advanced course in foundations of mathematics (2018/2019)

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 Peter Michael Schuster

Go to lesson schedule

Teoria 2 3 II semestre Daniel Wessel

Go to lesson schedule

Learning outcomes

This monographic course introduces advanced topics in the area of the foundations of mathematics and discusses their repercussions in mathematical practice. The specific arguments are detailed in the programme. At the end of this course the student will know advanced topics related to the foundations of mathematics. The student will be able to reflect upon their interactions with other disciplines of mathematics and beyond; to produce rigorous argumentations and proofs; and to read related articles and monographs, including advanced ones.


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

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

Reference books
Activity Author Title Publisher Year ISBN Note
Teoria 1 Torkel Franzén Gödel's Theorem: An Incomplete Guide to its Use and Abuse. A K Peters, Ltd. 2005 1-56881-238-8
Teoria 1 Jon Barwise (ed.) Handbook of Mathematical Logic North-Holland 1977 0-444-86388-5
Teoria 1 Riccardo Bruni Kurt Gödel, un profilo. Carocci 2015 9788843075133
Teoria 1 Peter Aczel, Michael Rathjen Notes on Constructive Set Theory 2010
Teoria 1 Yiannis N. Moschovakis Notes on Set Theory Springer 1994 978-1-4757-4155-1

Student opinions - 2017/2018