Table of contents

Set Theory from ZFC to Forcing

A graduate path from axiomatic foundations to modern independence methods

Read each section in order. Every title can be opened as a TheoryTrace document.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: The Axiomatic View of Sets
• Chapter 2: Classes, Relations, and Recursion
• Chapter 3: Well-Orderings and Ordinals
• Chapter 4: Cardinals and Cardinal Arithmetic
• Chapter 5: The Cumulative Hierarchy and Rank
• Chapter 6: Choice Principles and Their Equivalents
• Chapter 7: Filters, Ideals, and Boolean Algebras
• Chapter 8: Models of Set Theory
• Chapter 9: Absoluteness and Reflection
• Chapter 10: Constructibility and the Universe L
• Chapter 11: Independence and Relative Consistency
• Chapter 12: Forcing: Posets, Names, and Generic Extensions
• Chapter 13: The Forcing Theorem and Preservation
• Chapter 14: Classical Forcing Constructions
• Chapter 15: Iterated Forcing
• Chapter 16: Combinatorial Set Theory
• Chapter 17: Large Cardinals
• Chapter 18: Descriptive Set Theory and Regularity
• Chapter 19: Advanced Independence Phenomena
• Chapter 20: The Set-Theoretic Multiverse and Foundations
• Conclusion