Combinatorial Set Theory With a Gentle Introduction to Forcing

Combinatorial Set Theory With a Gentle Introduction to Forcing / by Lorenz J. Halbeisen.

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...

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Bibliographic Details
Main Author: Halbeisen, Lorenz J. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: London : Springer London : Imprint: Springer, 2012.
Edition:1st ed. 2012.
Series:Springer Monographs in Mathematics,
Springer eBook Collection.
Subjects:
Mathematical logic.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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