Combinatorial Set Theory With a Gentle Introduction to Forcing /

• Main Author: Halbeisen, Lorenz J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2012.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Mathematical logic.; Mathematical Logic and Foundations.

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophi...

Table of Contents:

• The Setting
• Overture: Ramsey's Theorem
• The Axioms of Zermelo-Fraenkel Set Theory
• Cardinal Relations in ZF only
• The Axiom of Choice
• How to Make Two Balls from One
• Models of Set Theory with Atoms
• Twelve Cardinals and their Relations
• The Shattering Number Revisited
• Happy Families and their Relatives
• Coda: A Dual Form of Ramsey's Theorem
• The Idea of Forcing
• Martin's Axiom
• The Notion of Forcing
• Models of Finite Fragments of Set Theory
• Proving Unprovability
• Models in which AC Fails
• Combining Forcing Notions
• Models in which p = c
• Properties of Forcing Extensions
• Cohen Forcing Revisited
• Silver-Like Forcing Notions
• Miller Forcing
• Mathias Forcing
• On the Existence of Ramsey Ultrafilters
• Combinatorial Properties of Sets of Partitions
• Suite.