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Set theory : exploring independence and truth / Ralf Schindler.

By: Material type: TextTextSeries: UniversitextPublication details: New York : Springer, 2014.Description: x, 332 p. ; illustrationsISBN:
  • 9783319067247
Subject(s): DDC classification:
  • 511.322 23 Sch336
Contents:
1. Naive set theory -- 2. Axiomatic set theory -- 3. Ordinals -- 4. Cardinals -- 5. Constructibility -- 6. Forcing -- 7. Descriptive set theory -- 8. Solovay's model -- 9. The Raisonnier filter -- 10. Measurable cardinals -- 11. 0[superscript]# and Jensen's covering lemma -- 12. Analytic and full determinacy -- 13. Projective determinacy-- References-- Index.
Summary: 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 511.322 Sch336 (Browse shelf(Opens below)) Available 135800
Total holds: 0

Includes bibliographical references and index.

1. Naive set theory --
2. Axiomatic set theory --
3. Ordinals --
4. Cardinals --
5. Constructibility --
6. Forcing --
7. Descriptive set theory --
8. Solovay's model --
9. The Raisonnier filter --
10. Measurable cardinals --
11. 0[superscript]# and Jensen's covering lemma --
12. Analytic and full determinacy --
13. Projective determinacy--

References--
Index.

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.

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