<電子ブック>
A Guide to Classical and Modern Model Theory / by Annalisa Marcja, Carlo Toffalori
(Trends in Logic, Studia Logica Library. ISSN:22127313 ; 19)
版 | 1st ed. 2003. |
---|---|
出版者 | (Dordrecht : Springer Netherlands : Imprint: Springer) |
出版年 | 2003 |
本文言語 | 英語 |
大きさ | XI, 371 p : online resource |
著者標目 | *Marcja, Annalisa author Toffalori, Carlo author SpringerLink (Online service) |
件 名 | LCSH:Logic LCSH:Mathematical logic LCSH:Algebra FREE:Logic FREE:Mathematical Logic and Foundations FREE:Algebra |
一般注記 | Structures -- 1.1 Structures -- 1.2 Sentences -- 1.3 Embeddings -- 1.4 The Compactness Theorem -- 1.5 Elementary classes and theories -- 1.6 Complete theories -- 1.7 Definable sets -- 1.8 References -- Quantifier Elimination -- 2.1 Elimination sets -- 2.2 Discrete linear orders -- 2.3 Dense linear orders -- 2.4 Algebraically closed fields (and Tarski) -- 2.5 Tarski again: Real closed fields -- 2.6 pp-elimination of quantifiers and modules -- 2.7 Strongly minimal theories -- 2.8 o-minimal theories -- 2.9 Computational aspects of q. e -- 2.10 References -- Model Completeness -- 3.1 An introduction -- 3.2 Abraham Robinson’s test -- 3.3 Model completeness and Algebra -- 3.4 p-adic fields and Artin’s Conjecture -- 3.5 Existentially closed structures -- 3.6 DCF0 -- 3.7 SCFp and DCFp -- 3.8 ACFA -- 3.9 References -- Elimination of imaginaries -- 4.1 Interpretability -- 4.2 Imaginary elements -- 4.3 Algebraically closed fields -- 4.4 Real closed fields -- 4.5 The elimination of imaginaries sometimes fails -- 4.6 References -- Morley rank -- 5.1 A tale of two chapters -- 5.2 Definable sets -- 5.3 Types -- 5.4 Saturated models -- 5.5 A parenthesis: pure injective modules -- 5.6 Omitting types -- 5.7 The Morley rank, at last -- 5.8 Strongly minimal sets -- 5.9 Algebraic closure and definable closure -- 5.10 References -- ? -stability -- 6.1 Totally transcendental theories -- 6.2 ?-stable groups -- 6.3 ?-stable fields -- 6.4 Prime models -- 6.5 DCF0 revisited -- 6.6 Ryll-Nardzewski’s Theorem, and other things -- 6.7 References -- Classifying -- 7.1 Shelah’s Classification Theory -- 7.2 Simple theories -- 7.3 Stable theories -- 7.4 Superstable theories -- 7.5 ?-stable theories -- 7.6 Classifiable theories -- 7.7 Shelah’s Uniqueness Theorem -- 7.8 Morley’s Theorem -- 7.9 Biinterpretability and Zilber Conjecture -- 7.10 Two algebraicexamples -- 7.11 References -- Model Theory and Algebraic Geometry -- 8.1 Introduction -- 8.2 Algebraic varieties, ideals, types -- 8.3 Dimension and Morley rank -- 8.4 Morphisms and definable functions -- 8.5 Manifolds -- 8.6 Algebraic groups -- 8.7 The Mordell-Lang Conjecture -- 8.8 References -- O-minimality -- 9.1 Introduction -- 9.2 The Monotonicity Theorem -- 9.3 Cells -- 9.4 Cell decomposition and other theorems -- 9.5 Their proofs -- 9.6 Definable groups in o-minimal structures -- 9.7 O-minimality and Real Analysis -- 9.8 Variants on the o-minimal theme -- 9.9 No rose without thorns -- 9.10 References Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world. This volume: -is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic HTTP:URL=https://doi.org/10.1007/978-94-007-0812-9 |
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 | 9789400708129 |
|
電子リソース |
|
EB00234588 |
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:8回
※2017年9月4日以降