Set theory

Thomas Jech

This monograph covers the recent major advances in various areas of set theory. From the reviews: "One of the classical textbooks and reference books in set theory...The present 'Third Millennium' edition...is a whole new book. In three parts the author offers us what in his view every young set theorist should learn and master...This well-written book promises to influence the next generation of set theorists, much as its predecessor has done." --MATHEMATICAL REVIEWS

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[目次]

  • Basic Set Theory.- Axioms of Set Theory.- Ordinal Numbers.- Cardinal Numbers.- Real Numbers.- The Axiom of Choice and Cardinal Arithmetic.- The Axiom of Regularity.- Filters, Ultrafilters and Boolean Algebras.- Stationary Sets.- Combinatorial Set Theory.- Measurable Cardinals.- Borel and Analytic Sets.- Models of Set Theory.- Advanced Set Theory.- Constructible Sets.- Forcing.- Applications of Forcing.- Iterated Forcing and Martin's Axiom.- Large Cardinals.- Large Cardinals and L.- Iterated Ultrapowers and L[U].- Very Large Cardinals.- Large Cardinals and Forcing.- Saturated Ideals.- The Nonstationary Ideal.- The Singular Cardinal Problem.- Descriptive Set Theory.- The Real Line.- Selected Topics.- Combinatorial Principles in L.- More Applications of Forcing.- More Combinatorial Set Theory.- Complete Boolean Algebras.- Proper Forcing.- More Descriptive Set Theory.- Determinacy.- Supercompact Cardinals and the Real Line.- Inner Models for Large Cardinals.- Forcing and Large Cardinals.- Martin's Maximum.- More on Stationary Sets.

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この本の情報

書名 Set theory
著作者等 Jech, Thomas J.
シリーズ名 Springer monographs in mathematics
出版元 Springer
刊行年月 c2003
版表示 3rd millennium ed., rev. and expanded
ページ数 xiii, 769 p.
大きさ 25 cm
ISBN 3540440852
NCID BA59605072
※クリックでCiNii Booksを表示
言語 英語
出版国 ドイツ
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