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Set Theory : Exploring Independence and Truth.
・ISBN 978-3-319-06724-7 paper EUR 79.99
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| 著者・編者 | Schindler, Ralf, |
|---|---|
| シリーズ | Universitext |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2014 |
| ページ数 | 332 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-21751＞ |
解説
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.