Fast Track to Forcing

For those who wonder if the forcing theory is beyond their means: no. Directions to research in forcing are given.

Mirna Džamonja (Author)

9781108413145, Cambridge University Press

Paperback / softback, published 15 October 2020

200 pages
23 x 15.3 x 1 cm, 0.25 kg

This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.

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: 10. Introduction to Part Two
11. Classical Extensions
12. Iterated Forcing and Martin's Axiom
13. Some More Large Cardinals
14. Limitations of Martin's Axiom and Countable Supports
15. Proper Forcing and PFA
16. $aleph_2$ and other Successors of Regulars
17. Singular Cardinal Hypothesis and some PCF
18. Forcing at Singular Cardinals and their Successors
References
Index.

Subject Areas: Set theory [PBCH], Mathematical logic [PBCD]