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Combinatorial set theory = with a gentle introduction to forcing /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Combinatorial set theory/ by Lorenz J. Halbeisen.
其他題名:	with a gentle introduction to forcing /
作者:	Halbeisen, Lorenz J.
出版者:	Cham :Springer International Publishing : : 2017.,
面頁冊數:	xvi, 594 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Combinatorial set theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-60231-8
ISBN:	9783319602318

Combinatorial set theory = with a gentle introduction to forcing /
Halbeisen, Lorenz J.

Combinatorial set theorywith a gentle introduction to forcing /[electronic resource] :by Lorenz J. Halbeisen. - 2nd ed. - Cham :Springer International Publishing :2017. - xvi, 594 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

The Setting -- First-Order Logic in a Nutshell -- Axioms of Set Theory -- Overture: Ramsey's Theorem -- Cardinal Relations in ZF Only -- Forms of Choice -- How to Make Two Balls from One -- Models of Set Theory with Atoms -- Thirteen Cardinals and Their Relations -- The Shattering Number Revisited -- Happy Families and Their Relatives -- Coda: A Dual Form of Ramsey's Theorem -- The Idea of Forcing -- Martin's Axiom -- The Notion of Forcing -- Proving Unprovability -- Models in Which AC Fails -- Combining Forcing Notions -- Models in Which p=c -- Suslin's Problem -- Properties of Forcing Extensions -- Cohen Forcing Revisited -- Sacks Forcing -- Silver-Like Forcing Notions -- Miller Forcing -- Mathias Forcing -- How Many Ramsey Ultrafilters Exist? -- Combinatorial Properties of Sets of Partitions -- Suite.

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.

ISBN: 9783319602318

Standard No.: 10.1007/978-3-319-60231-8doiSubjects--Topical Terms:

888936
Combinatorial set theory.

LC Class. No.: QA248 / .H35 2017

Dewey Class. No.: 511.322

Combinatorial set theory = with a gentle introduction to forcing /
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505 0 $a The Setting -- First-Order Logic in a Nutshell -- Axioms of Set Theory -- Overture: Ramsey's Theorem -- Cardinal Relations in ZF Only -- Forms of Choice -- How to Make Two Balls from One -- Models of Set Theory with Atoms -- Thirteen Cardinals and Their Relations -- The Shattering Number Revisited -- Happy Families and Their Relatives -- Coda: A Dual Form of Ramsey's Theorem -- The Idea of Forcing -- Martin's Axiom -- The Notion of Forcing -- Proving Unprovability -- Models in Which AC Fails -- Combining Forcing Notions -- Models in Which p=c -- Suslin's Problem -- Properties of Forcing Extensions -- Cohen Forcing Revisited -- Sacks Forcing -- Silver-Like Forcing Notions -- Miller Forcing -- Mathias Forcing -- How Many Ramsey Ultrafilters Exist? -- Combinatorial Properties of Sets of Partitions -- Suite.
520 $a 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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