Axiomatic set theory for mathematical practice (2019/2020)

Course code
4S009160
Name of lecturer
Peter Michael Schuster
Coordinator
Peter Michael Schuster
Number of ECTS credits allocated
4
Academic sector
MAT/01 - MATHEMATICAL LOGIC
Language of instruction
English
Location
VERONA
Period
2° semestre Scienze e Ingegneria dal Mar 2, 2020 al May 9, 2020.

Lesson timetable

Go to lesson schedule

Learning outcomes

This monographic course introduces advanced topics in the area of axiomatic set theory and discusses their use in mathematical practice. The specific arguments are detailed in the programme. At the end of this course the student will know advanced material about the topics of the course. The student, moreover, will be able to reflect upon the use of this material in mathematical practice; to produce rigorous argumentations and proofs; and to read related articles and monographs, including advanced ones.

Syllabus

Introduction to Zermelo-Fraenkel style axiomatic set
theory with particular regard to mathematical practice, including
aspects of (non)constructivity and (im)predicativity, as well as
transfinite proof methods: Axiom of Choice, Well-Ordering Theorem,
Zorn's Lemma, etc.

Reference books
Author Title Publisher Year ISBN Note
Abrusci, Vito Michele & Tortora de Falco, Lorenzo Logica. Volume 2 - Incompletezza, teoria assiomatica degli insiemi. Springer 2018 978-88-470-3967-4
Peter Aczel, Michael Rathjen Notes on Constructive Set Theory 2010
Yiannis N. Moschovakis Notes on Set Theory Springer 1994 978-1-4757-4155-1

Assessment methods and criteria

Written essay with presentation and discussion in class.