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.
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.
|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|
Written essay with presentation and discussion in class.
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