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
4 - Well Orderings and Ordinals
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
We start with a lemma that gives an equivalent definition of a well ordering, and which is often used in practice when we check whether a set is well ordered or not. We use the notation (L, <) of the strict order and (L, ≤) of the order which is not necessarily strict, interchangeably, since each of these objects is induced by the other. All theorems in the theory of order translate between these versions in a straightforward manner.
- Type
- Chapter
- Information
- Fast Track to Forcing , pp. 17 - 25Publisher: Cambridge University PressPrint publication year: 2020