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Combinatorial Set Theory - With a Gentle Introduction to Forcing (Hardcover, 2nd ed. 2017)
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Combinatorial Set Theory - With a Gentle Introduction to Forcing (Hardcover, 2nd ed. 2017)
Series: Springer Monographs in Mathematics
Expected to ship within 12 - 17 working days
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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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