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Axiomatic Set Theory (Paperback, 1973 ed.)
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Axiomatic Set Theory (Paperback, 1973 ed.)
Series: Graduate Texts in Mathematics, 8
Expected to ship within 18 - 22 working days
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This text deals with three basic techniques for constructing models
of Zermelo-Fraenkel set theory: relative constructibility, Cohen's
forcing, and Scott-Solovay's method of Boolean valued models. Our
main concern will be the development of a unified theory that
encompasses these techniques in one comprehensive framework.
Consequently we will focus on certain funda mental and intrinsic
relations between these methods of model construction. Extensive
applications will not be treated here. This text is a continuation
of our book, "I ntroduction to Axiomatic Set Theory,"
Springer-Verlag, 1971; indeed the two texts were originally planned
as a single volume. The content of this volume is essentially that
of a course taught by the first author at the University of
Illinois in the spring of 1969. From the first author's lectures, a
first draft was prepared by Klaus Gloede with the assistance of
Donald Pelletier and the second author. This draft was then rcvised
by the first author assisted by Hisao Tanaka. The introductory
material was prepared by the second author who was also responsible
for the general style of exposition throughout the text. We have
inc1uded in the introductory material al1 the results from Boolean
algebra and topology that we need. When notation from our first
volume is introduced, it is accompanied with a deflnition, usually
in a footnote. Consequently a reader who is familiar with
elementary set theory will find this text quite self-contained.
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