Set Theory

Exploring Independence and Truth

By: Ralf Schindler

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Paperback | 6 June 2014

At a Glance

Paperback
344 Pages

Dimensions(cm)
22.86 x 15.24 x 1.91

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$139.00

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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.

Industry Reviews

"A book like this is not only useful, it is necessary for set theory. It contains great results, some of the most celebrated in set theory, it finally has a comprehensive exposition of many essential tools ... this is the perfect book for someone who already is familiar with set theory, and wants to know more about this specific part. It is also a good introduction for somebody who comes from outside set theory, but is curious about it." (Vincenzo Dimonte, Studia Logica, Vol. 106, 2018)

"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)

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