Set Theory Exploring Independence and Truth /

• Κύριος συγγραφέας: Schindler, Ralf (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Mathematical logic.; Mathematical Logic and Foundations.

 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. 

 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.