CODE 61711 2023/2024 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA MAT/01 Italian (English on demand) GENOVA 2° Semester AULAWEB

OVERVIEW

The lecture course introduces to set theory in its axiomatic form, by explicitly listing basic axioms and, from those, deriving basic theorems which are of major relevance for the mathematical practice. Then the course will be devoted to the development of appropriate techniques to get to independence proofs.

AIMS AND CONTENT

LEARNING OUTCOMES

Introduction to set theory as a foundation of mathematics.

AIMS AND LEARNING OUTCOMES

At the end of the lecture course, a student has improved one's awareness of the mathematical facts and one's own understanding abilities of themes in mathematics in order to

• use them effectively to produce judgements autonomously;
• improve one's communication abilities in mathematics;
• strengthen one's power to learn and to analize mathematical themes.

The course considers set theory as useful fonudation in the practice and didactics of mathematics, and presents the main tools for its applications. The course develops the theory and applies it to mathematical practice, also by means of examples from the students' previous experience.

PREREQUISITES

None, it may be useful to have proficiency in mathematical proofs.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

The course will be about some of the following, depending on specific requests of the attendees:

Axiomatic presentations of set theory: ZF and NBG, ordinals, cardinals
The axiom of foundations, equivalent forms
The axiom of choice, equivalent forms
Cantor's and Dedekind's constructions of the real numbers, the continuum hypothesis
Models of ZF, relativization, relative consistency, constructible sets, inaccessible cardinals
Boolean-valued models, independence proofs

Elliott Mendelson, Introduzione alla logica matematica. Boringhieri 1975

Thomas Jech, Set Theory. The third millenium edition, Springer 2002

John Bell, Set Theory. Boolean-valued Models and Independence Proofs, Oxford University Press 1984

TEACHERS AND EXAM BOARD

Exam Board

GIUSEPPE ROSOLINI (President)

JACOPO EMMENEGGER

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.

EXAMS

EXAM DESCRIPTION

The exam consists of a written essay and of an oral examination which can be taken in either order. The written essay is on the arguments of the lecture course and asks for the presentation of particular subjects taught in the course and the solution of exercises. The oral examination is a presentation and an open discussion on subjects in the syllabus. The final mark determines how the two tests complement each other. The oral examination can be taken in itinere.

ASSESSMENT METHODS

The written essay verifies the actual acquisition of the mathematical knowledge of set theory and determines the skills developed to use such knowledge by means of problems and open questions. The oral examination consists mainly in a presentation of some part of the syllabus and aims at evaluating that the student has acquired an appropriate level of knowledge and analytical skills.

Students with DSA (=Specific Learning Disabilities), certification 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.

Exam schedule

Data Ora Luogo Degree type Note
03/06/2024 09:00 GENOVA Esame su appuntamento