Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Let’s Be Independent
- 1 Introduction
- 2 Axiomatic Systems
- 3 Zermelo–Fraenkel Axioms and the Axiom of Choice
- 4 Well Orderings and Ordinals
- 5 Cardinals
- 6 Models and Independence
- 7 Some Class Models of ZFC
- 8 Forcing
- 9 Violating CH
- Part II What is New in Set Theory
- References
- Index
3 - Zermelo–Fraenkel Axioms and the Axiom of Choice
from Part I - Let’s Be Independent
Published online by Cambridge University Press: 28 September 2020
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Let’s Be Independent
- 1 Introduction
- 2 Axiomatic Systems
- 3 Zermelo–Fraenkel Axioms and the Axiom of Choice
- 4 Well Orderings and Ordinals
- 5 Cardinals
- 6 Models and Independence
- 7 Some Class Models of ZFC
- 8 Forcing
- 9 Violating CH
- Part II What is New in Set Theory
- References
- Index
Summary
Every axiomatic system has its basic objects and relations and the axioms that describe these objects. Let us go back to the example of Euclidean geometry and develop further what we said about it in the previous chapter: the basic objects of Euclidean geometry are points, lines and planes. They are not defined. The basic relationship between these objects is the relation of incidence or membership. There are five axioms, for example:
- Type
- Chapter
- Information
- Fast Track to Forcing , pp. 8 - 16Publisher: Cambridge University PressPrint publication year: 2020