Set Theory

Exploring Independence and Truth

AvRalf Schindler

Häftad, Engelska, 2014

Del i serien Universitext

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2014-06-06
Mått:155 x 235 x 19 mm
Vikt:522 g
Format:Häftad
Språk:Engelska
Serie:Universitext
Antal sidor:332
Upplaga:2014
Förlag:Springer International Publishing AG
ISBN:9783319067247

Utforska kategorier

Matematikens grunder inom Naturvetenskap och teknik

Mer om författaren

Ralf Schindler teaches at Universität Münster and is an expert in the field of set theory.Ralf Schindler works mostly in the area of descriptive inner model theory. His results are on the construction of inner models and core models, on coding over core models and on applications of inner model theory to descriptive set theory and combinatorics. He isolated the concept of a “remarkable” cardinal.

Recensioner i media

"This text is, in its own way, a remarkable accomplishment. While a 'Universitext', it somehow manages to pursue a steady path of exposition from the beginnings in the seminal work of Cantor through to Jensen's covering Lemma and the Martin-Steel Theorem on Projective Determinacy. ... this text could well be considered an informative one even for the set theorist." (A. Kanamori, Mathematical Reviews, June, 2015) "The material is given in a form that is accessible to students. ... The book contains many interesting problems which help the reader to follow and understand the presented material. This very carefully written book can be recommended to everyone seriously interested in modern set theory." (Martin Weese, zbMATH, Vol. 1296, 2014)

Innehållsförteckning

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.