# Set Theory

From Wikibooks, open books for an open world

Set theory is concerned with the concept of a set, essentially a collection of objects that we call elements. Because of its generality, set theory forms the foundation of nearly every other part of mathematics.

## Before you begin

In order to make things easier for you as a reader, as well as for the writers, you will be expected to be familiar with a few topics before beginning. (I hope to have some links to other Wikibooks here soon.)

- Mathematical Logic & Proofs
- Mathematics is all about proofs. One of the goals of this book is to improve your skills at making proofs, but you will not learn any of the basics here.
- Many constructions in set theory are simply generalizations of constructions in mathematical logic, and therefore logic is a necessity of learning set theory.

## Set theory

- Sets
- Axioms
- Relations
- Orderings
- Zorn's Lemma and the Axiom of Choice
- Ordinals
- Cardinals
- Zermelo-Fraenkel Axiomatic Set Theory

- Appendix 1. Naive Set Theory
- Review

## Further reading

- Discrete Mathematics/Set theory
- Krzysztof Ciesielski,
*Set Theory for the Working Mathematician*(1997) - P. R. Halmos,
*Naive Set Theory*(1974) - Karel Hrbacek, Thomas J. Jech,
*Introduction to set theory*(1999) - Thomas J. Jech,
*Set Theory*3rd Edition (2006) - Kenneth Kunen,
*Set Theory: an introduction to independence proofs*(1980) - Judith Roitman,
*Introduction to Modern Set Theory*(1990) - John H. Conway, Richard Guy
*The Book of Numbers*- chapter 10 - Tobias Dantzig, Joseph Mazur
*Number: The Language of Science*