CODE 108961 2022/2023 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA MAT/01 GENOVA 2° Semester AULAWEB

## 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 the study of 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.

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

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

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

K. Hrbacek, T. Jech, Introduction to set theory, Dekker 1999.

A.S. Kechris, Classical descriptive set theory, Springer 1995.

## TEACHERS AND EXAM BOARD

### Exam Board

RICCARDO CAMERLO (President)

SARA NEGRI

GIUSEPPE ROSOLINI (President Substitute)

## LESSONS

### 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 replace by exercises proposed during lectures.

Students with DSA certification («specific learning disabilities»), disability or other special educational needs are advised to contact the teacher at the beginning of the course to establish on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

### ASSESSMENT METHODS

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