Combinatorial Set Theory : With a Gentle Introduction to Forcing
Second Edition 2017
Book Details
Format
Paperback / Softback
Book Series
Springer Monographs in Mathematics
ISBN-10
3319868128
ISBN-13
9783319868127
Edition
Second Edition 2017
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 4th, 2019
Print length
594 Pages
Weight
902 grams
Dimensions
23.40 x 15.70 x 3.60 cms
Product Classification:
Mathematical foundationsMathematical logicDiscrete mathematics
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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 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 self-study.
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