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 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.
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