Set theory : exploring independence and truth
著者
書誌事項
Set theory : exploring independence and truth
（Universitext）
Springer, c2014
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注記
Includes bibliographical reference (p. 325-326) and index
内容説明・目次
内容説明
This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory.
The following topics are covered:
* Forcing and constructability
* The Solovay-Shelah Theorem i.e. the equiconsistency of 'every set of reals is Lebesgue measurable' with one inaccessible cardinal
* Fine structure theory and a modern approach to sharps
* Jensen's Covering Lemma
* The equivalence of analytic determinacy with sharps
* The theory of extenders and iteration trees
* A proof of projective determinacy from Woodin cardinals.
Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
目次
Naive set theory.- Axiomatic set theory.- Ordinals.- Cardinals.- Constructability.- Forcing.- Descriptive set theory.- Solovay's model.- The Raisonnier filter.- Measurable cardinals.- 0# and Jensen's Covering Lemma.- Analytic and full determinacy.- Projective determinacy.
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