Author 
Halbeisen, Lorenz J.

Series 
Springer monographs in mathematics, 14397382 

Springer monographs in mathematics.

Subject 
Combinatorial set theory.


Forcing (Model theory)


Mathematics.

Description 
1 online resource (xvi, 453 pages) 
Bibliography Note 
Includes bibliographical references and index. 
Contents 
The Setting  Overture: Ramsey's Theorem  The Axioms of ZermeloFraenkel 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  SilverLike Forcing Notions  Miller Forcing  Mathias Forcing  On the Existence of Ramsey Ultrafilters  Combinatorial Properties of Sets of Partitions  Suite. 
Summary 
This book provides a selfcontained 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 sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field. 
Note 
English. 
ISBN 
9781447121732 (electronic bk.) 

1447121732 (electronic bk.) 

1447121724 (print) 

9781447121725 (print) 

9781447160861 (print) 

144716086X 

9781447121749 (print) 

1447121740 

9781447121725 
ISBN/ISSN 
10.1007/9781447121732 
OCLC # 
765949043 
Additional Format 
Printed edition: 9781447121725 
