Set Theory: Exploring Independence and Truth: Universitext
Autor Ralf Schindleren Limba Engleză Paperback – 6 iun 2014
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.
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Specificații
ISBN-13: 9783319067247
ISBN-10: 3319067249
Pagini: 344
Ilustrații: X, 332 p. 10 illus.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.48 kg
Ediția:2014
Editura: Springer International Publishing
Colecția Springer
Seria Universitext
Locul publicării:Cham, Switzerland
ISBN-10: 3319067249
Pagini: 344
Ilustrații: X, 332 p. 10 illus.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.48 kg
Ediția:2014
Editura: Springer International Publishing
Colecția Springer
Seria Universitext
Locul publicării:Cham, Switzerland
Public țintă
GraduateCuprins
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.
Recenzii
“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)
“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)
Notă biografică
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.
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.
Textul de pe ultima copertă
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.
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.
Caracteristici
Provides a fairly self-contained introduction to set theory, in particular to the theory of inner models and forcing Presents essential aspects of set theory which are required in understanding modern developments of descriptive inner model theory Includes proofs of landmark results at the interface of the theory of large cardinals and descriptive set theory Includes supplementary material: sn.pub/extras