## SET THEORY

Teachers

##### Vincenzo Dimonte
6
First Period
###### Course Type
Supplementary
Prerequisites. Basic knowledge about ZFC (e.g. those given in the Mathematical Logic course of the laurea triennale)
Teaching Methods. Traditional teaching with examples and exercises.
Verification of Learning. Oral exam of about 40 minutes. The student needs to show understanding of the topics and rove some of the main theorems seen during the course.
##### Objectives
To know the fundamental topics and to learn the main techniques of set theory, such as cardinal arithmetic, large cardinals, Martin’s axiom, absoluteness, constructible sets, forcing and independence results.

To develop notions and techniques which can be used both inside set theory and in other areas of contemporary mathematics.

##### Contents
The axiom of choice, the continuum hypothesis, regular and singular cardinals;

Mostowski collapse and elementary relative consistency proofs;

the reflection theorem;

constructible sets and consistency of AC and GCH;

Martin axiom;

forcong and consistency of not CH, CH + not GCH, and diamond.

##### Texts
Notes taken during the lectures. In addition, the following texts can be useful:

K. Kunen, Set Theory. An Introduction to Independence Proofs, North-Holland, 1980

K. Kunen, Set Theory, College Publications, 2011 (the “new” edition of the previous text)

K. Cieselski, Set Theory for the Working Mathematician, Cambridge UP, 1997

T. Jech, Set theory. The third millenium edition, Springer, 2003