Set theory
著者
書誌事項
Set theory
（Springer monographs in mathematics）
Springer, c2003
3rd millennium ed., rev. and expanded
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注記
Includes bibliographical references (p. [707]-732) and indexes
"Corrected 4th printing 2006"--T.p. verso of [4th print.]
内容説明・目次
内容説明
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
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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