Author 
Halbeisen, Lorenz J.,

Series 
Springer monographs in mathematics 

Springer monographs in mathematics.

Subject 
Combinatorial set theory.


Forcing (Model theory)

Description 
1 online resource. 

polychrome rdacc 
Edition 
Second edition. 
Bibliography Note 
Includes bibliographical references and indexes. 
Contents 
The Setting  FirstOrder 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  SilverLike Forcing Notions  Miller Forcing  Mathias Forcing  How Many Ramsey Ultrafilters Exist?  Combinatorial Properties of Sets of Partitions  Suite. 
Summary 
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 firstorder logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin's problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah's astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for selfstudy. 

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 firstorder logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslins problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelahs astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, 㯭mbinatorial Set Theory穬l appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for selfstudy. 
Note 
Vendorsupplied metadata. 
ISBN 
9783319602318 (electronic bk.) 

3319602314 (electronic bk.) 

9783319602301 

3319602306 

9783319602301 
ISBN/ISSN 
10.1007/9783319602318 
OCLC # 
1017736581 
Additional Format 
Printed edition: 9783319602301 
