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Combinatorial Set Theory: With a Gentle Introduction to Forcing (Springer Monographs in Mathematics)
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Combinatorial Set Theory: With a Gentle Introduction to Forcing (Springer Monographs in Mathematics)
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Taschenbuch. Condizione: Neu. Combinatorial Set Theory | With a Gentle Introduction to Forcing | Lorenz J. Halbeisen | Taschenbuch | Springer Monographs in Mathematics | xvii | Englisch | 2026 | Springer | EAN 9783031917547 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[do…t]hartmann[at]springer[dot]com | Anbieter: preigu.
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Taschenbuch. Condizione: Neu. Combinatorial Set Theory | With a Gentle Introduction to Forcing | Lorenz J. Halbeisen | Taschenbuch | xvi | Englisch | 2019 | Springer | EAN 9783319868127 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbie…ter: preigu.
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice an…d Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
Combinatorial Set Theory: With a Gentle Introduction to Forcing (Springer Monographs in Mathematics)
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Combinatorial Set Theory: With a Gentle Introduction to Forcing (Springer Monographs in Mathematics)
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Serie: Libro 149 di 187 - Springer Monographs in Mathematics
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of…classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin's problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah's astonishing construction of a model with finitely many Ramsey ultrafilters.Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory.After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axio…ms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah s astonishing construction of a model with finitely many Ramsey ultrafilters is given.Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study.
Combinatorial Set Theory: With a Gentle Introduction to Forcing (Springer Monographs in Mathematics)
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the ax…iom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field. 472 pp. Englisch.
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory.Following an overview of basic notions in combinatorics and first-order logic, the author outlines the… main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin's problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah's astonishing construction of a model with finitely many Ramsey ultrafilters.Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study. 612 pp. Englisch.
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory.After an overview of basic notions in combinatorics and first-order logic, and discussing i…n great detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah s astonishing construction of a model with finitely many Ramsey ultrafilters is given.Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study. 636 pp. Englisch.
Lingua: Inglese
Editore: Springer Nature Switzerland, Springer International Publishing Mai 2025, 2025
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Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermaniaBuchWeltWeit Ludwig Meier e.K.
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory.After an overview of basic notions in combinatorics and first-order logic, and discussing in great… detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah s astonishing construction of a model with finitely many Ramsey ultrafilters is given.Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study. 636 pp. Englisch.
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory.After an overview of basic notions in combinatorics and first-order logic, and discussing in gr…eat detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah's astonishing construction of a model with finitely many Ramsey ultrafilters is given.Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study. 636 pp. Englisch.
Lingua: Inglese
Editore: Springer, Springer Nature Switzerland Mai 2025, 2025
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 636 pp. Englisch.
