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Set Theory : Exploring Independence and Truth / by Ralf Schindler
Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Universitext | SpringerLink BücherPublisher: Cham [u.a.] : Springer, 2014Description: Online-Ressource (X, 332 p. 10 illus, online resource)ISBN:- 9783319067254
- 511.3
- QA8.9-10.3
Contents:
Summary: 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 determinacySummary: 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 researchersPPN: PPN: 1657953505Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
Naive set theoryAxiomatic 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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