OVERVIEW

The course introduce set theory as foundational theory for mathematics. Then it presents some subjects peculiar to the theory, like ordinal and cardinal arithmetic, and provides some applications of them to algebra, topology, and analysis.

AIMS AND CONTENT

LEARNING OUTCOMES

Main goal of the course is to introduce and analyse the set theoretic constructions and their mathematical applications.

AIMS AND LEARNING OUTCOMES

At the end of the course, students will be able to deal with basic set theoretic operations, recognise the applicazions of set theoretic principles like the axiom of choince, be familiar with the concepts of order type of a well order and cardinality, and apply set-theoretic methods to various mathematical problems.

PREREQUISITES

Familiarity with basic mathematical notions from algebra, analysis, and topology.

TEACHING METHODS

Class lectures.

SYLLABUS/CONTENT

1. Review of the notion of a set and of basic set theoretic operations
2. Construction of number sets
3. The axiomatisation of set theory
4. The axiom of choice and its equivalents
5. Ordinals, cardinals, and their arithmetic
6. Descriptive set theory
7. Applications

RECOMMENDED READING/BIBLIOGRAPHY

The instructor's notes will be available. Other useful references are:

K. Ciesielski, Set theort for the working mathematician, Cambridge University Press 1997.

D.W. Cunningham, Set theory, Cambridge University Press 2016.

D. Goldrei, Classic set theory, Chapman & Hall 1996.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

February 23rd, 2026

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written exam. The written exam can be partially or totally replaced by exercises proposed during lectures or by an oral exam.

ASSESSMENT METHODS

The evaluation takes into account the correctedness of the solution to the exercises, the clarity of the exposition, and the rigour of the arguments.

FURTHER INFORMATION

Ask professor for other information not included in the teaching schedule.

Compensatory and dispensatory measures Disability/Invalidity/Specific Learning Disorder

Dispensatory measures and compensatory tools are intended to enable students to achieve the same learning objectives as their fellow students, not to facilitate the examination.

The use of compensatory tools and the application of dispensatory measures must be authorised in advance by the teacher in agreement with the Referee.

To take advantage of the adaptations during the examination, fill in the Adaptation request form; the request will be automatically sent by the system to the teacher in charge of the teaching, to the Contact Person of your School/Area/Department and in copy to the Sector; you will also receive a copy of the request sent by e-mail.

The adjustments available to students are as follows:

• Additional time (+30% DSA)
• Additional time (+50% disability/invalidity)
• Additional time during oral exams to organise the answer
• Calculator (programmable and graphing calculators are not allowed)
• Conceptual Maps
• Tables and/or Forms
• Take the exam in written form
• Take the exam in oral form
• Tutor reader (for written tests only)
• Tutor-writer (for written tests only)

Your request for adaptations must be submitted at least 7 working days before the scheduled exam date.

All information for students with disabilities and DSA is available on the webpage: Services for students with disabilities or DSA | UniGe | University of Genoa

Reference for inclusion: Sergio Di Domizio - sergio.didomizio@unige.it