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
5 - Cardinals
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
There is a natural order on the cardinals, induced from the ordinals. So, for example, 0 < 1 < 2 < … < ω < ω1. Notice that the order on the cardinals can also be defined by saying that κ < λ if there is an injection from κ to λ but not the other way around.
- Type
- Chapter
- Information
- Fast Track to Forcing , pp. 26 - 28Publisher: Cambridge University PressPrint publication year: 2020