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: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Mathematical logic.; Combinatorics.; Mathematical Logic and Foundations.

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including R...

Table of Contents:

• The Setting
• First-Order Logic in a Nutshell
• Axioms of Set Theory
• Overture: Ramsey's Theorem
• Cardinal Relations in ZF Only
• Forms of Choice
• How to Make Two Balls from One
• Models of Set Theory with Atoms
• Thirteen 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
• Proving Unprovability
• Models in Which AC Fails
• Combining Forcing Notions
• Models in Which p=c
• Suslin’s Problem
• Properties of Forcing Extensions
• Cohen Forcing Revisited
• Sacks Forcing
• Silver-Like Forcing Notions
• Miller Forcing
• Mathias Forcing
• How Many Ramsey Ultrafilters Exist?
• Combinatorial Properties of Sets of Partitions
• Suite.