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 SolovayShelah 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.

Hersteller:
Springer Verlag GmbH
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DE 69121 Heidelberg

InhaltsangabeNaive 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.