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
8 - Forcing
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
So far we have seen a way of building inner models of ZFC from the existing models. Forcing is a way of extending a given model of a portion of ZFC to another one. In fact, forcing is technically speaking, only applicable to countable transitive models (we shall discuss why later). The logic behind this process is as follows.
- Type
- Chapter
- Information
- Fast Track to Forcing , pp. 50 - 60Publisher: Cambridge University PressPrint publication year: 2020