# Introduction to Set Theory

## Objectives

Introduce set theory in an informal but sufficiently rigorous style. To emphasize the foundational character of set theory which derives from its great reducing and clarifying power in the most varied mathematical notions.

## General characterization

##### Code

10987

##### Credits

3.0

##### Responsible teacher

Manuel Messias Rocha de Jesus

##### Hours

Weekly - 3

Total - 36

##### Teaching language

Português

### Prerequisites

No requirements.

### Bibliography

1. H. B. Enderton. *Elements of Set Theory*. Academic Press, 1977.

2. A. J. Franco de Oliveira. *Teoria de Conjuntos*. Livraria Escolar Editora, 1982.

3. P. R. Halmos.* Naive Set Theory*. Springer, 1998.

4. T. Jech. *Set Theory: The Third Millennium Edition*, Revised and Expanded, Springer, 2002.

5. Y. Moschovakis. *Notes on Set Theory*. 2nd ed., Springer, 2006.

### Teaching method

Lectures + problem-solving sessions (3h00).

### Evaluation method

Students must attend, at least, 2/3 of classes.

Each student will be evaluated by two tests or an exam. More details in the portuguese version.

## Subject matter

Naïve set theory:

- Set operations,
- Relations and functions,
- Well-ordered sets and ordinals numbers,
- Finite arithmetic,
- Integers numbers, rational numbers and real numbers,
- Intuitive theory of cardinal numbers,
- Ordering cardinal numbers,
- Axiom of Choice, Zermelo’s Well-Ordering Theorem and Zorn’s Lemma,
- Cardinal arithmetic and Continuum Hypothesis,
- Paradoxes of Naïve Set Theory and Cumulative Hierarchy of sets.