<電子ブック>
Combinatorial Set Theory : With a Gentle Introduction to Forcing / by Lorenz J. Halbeisen
(Springer Monographs in Mathematics. ISSN:21969922)
版 | 2nd ed. 2017. |
---|---|
出版者 | Cham : Springer International Publishing : Imprint: Springer |
出版年 | 2017 |
本文言語 | 英語 |
大きさ | XVI, 594 p. 20 illus : online resource |
著者標目 | *Halbeisen, Lorenz J author SpringerLink (Online service) |
件 名 | LCSH:Mathematical logic LCSH:Discrete mathematics FREE:Mathematical Logic and Foundations FREE:Discrete Mathematics |
一般注記 | 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. Writtenfor 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 HTTP:URL=https://doi.org/10.1007/978-3-319-60231-8 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9783319602318 |
|
電子リソース |
|
EB00234449 |
書誌詳細を非表示
データ種別 | 電子ブック |
---|---|
分 類 | LCC:QA8.9-10.3 DC23:511.3 |
書誌ID | 4000120369 |
ISBN | 9783319602318 |
類似資料
この資料の利用統計
このページへのアクセス回数:6回
※2017年9月4日以降