图书介绍

数理逻辑教程 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

数理逻辑教程 英文
  • （英）贝尔著 著
  • 出版社： 北京：世界图书北京出版公司
  • ISBN：9787510086304
  • 出版时间：2015
  • 标注页数：599页
  • 文件大小：91MB
  • 文件页数：616页
  • 主题词：数理逻辑－教材－英文

PDF下载


点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快]温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页直链下载[便捷但速度慢]  [在线试读本书]   [在线获取解压码]
点击复制MD5值：31efcf338abba69caa574fc5dfaf1f62

下载说明

数理逻辑教程 英文PDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

点击复制85GB完整离线版磁力链接到迅雷FDM等BT下载工具进行下载  详情点击-查看共享计划
建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

图书目录

CHAPTER 0．PREREQUISITES1

CHAPTER 1．BEGINNING MATHEMATICAL LOGIC5

1．General considerations5

2．Structures and formal languages9

3．Higher-order languages14

4．Basic syntax15

5．Notational conventions18

6．Propositional semantics20

7．Propositional tableaux25

8．The Elimination Theorem for propositional tableaux31

9．Completeness of propositional tableaux33

10．The propositional calculus34

11．The propositional calculus and tableaux40

12．Weak completeness of the propositional calculus43

13．Strong completeness of the propositional calculus44

14．Propositionallogic based on ？ and∧46

15．Propositional logic based on？,→,∧and ∨47

16．Historical and bibliographical remarks48

CHAPTER 2．FIRST-ORDER LOGIC49

1．First-order semantics49

2．Freedom and bondage54

3．Substitution57

4．First-order tableaux67

5．Some"book-keeping"lemmas72

6．The Elimination Theorem for first-order tableaux79

7．Hintikka sets83

8．Completeness of first-order tableaux88

9．Prenex and Skolem forms93

10．Elimination of function symbols97

11．Elimination of equality101

12．Relativization102

13．Virtual terms104

14．Historical and bibliographical remarks107

CHAPTER 3．FIRST-ORDER LOGIC(CONTINUED)108

1．The first-order predicate calculus108

2．The first-order predicate calculus and tableaux115

3．Completeness of the first-order predicate calculus117

4．First-order logic based on 3122

5．What have we achieved?122

6．Historical and bibliographical remarks124

CHAPTER 4．BOOLEAN ALGEBRAS125

1．Lattices125

2．Boolean algebras129

3．Filters and homomorphisms133

4．The Stone Representation Theorem141

5．Atoms150

6．Duality for homomorphisms and continuous mappings153

7．The Rasiowa-Sikorski Theorem157

8．Historical and bibliographical remarks159

CHAPTER 5．MODEL THEORY161

1．Basic ideas of model theory161

2．The L？wenheim-Skolem Theorems168

3．Ultraproducts174

4．Completeness and categoricity184

5．Lindenbaum algebras191

6．Element types and ？-categoricity203

7．Indiscernibles and models with automorphisms214

8．Historical and bibliographical remarks224

CHAPTER 6．RECURSION THEORY226

1．Basic notation and terminology226

2．Algorithmic functions and functionals230

3．The computer URIM232

4．Computable functionals and functions237

5．Recursive functionals and functions239

6．A stockpile of examples247

7．Church's Thesis257

8．Recursiveness of computable functionals259

9．Functionals with several sequence arguments265

10．Fundamental theorems266

11．Recursively enumerable sets277

12．Diophantine relations284

13．The Fibonacci sequence288

14．The power function296

15．Bounded universal quantification305

16．The MRDP Theorem and Hilbert's Tenth Problem311

17．Historical and bibliographical remarks314

CHAPTER 7．LOGIC—LIMITATIVE RESULTS316

1．General notation and terminology316

2．Nonstandard models of Ω318

3．Arithmeticity324

4．Tarski's Theorem327

5．Axiomatic theories332

6．Baby arithmetic334

7．Junior arithmetic336

8．A finitely axiomatized theory340

9．First-order Peano arithmetic342

10．Undecidability347

11．Incompleteness353

12．Historical and bibliographical remarks359

CHAPTER 8．RECURSION THEORY(CONTINUED)361

1．The arithmetical hierarchy361

2．A result concerning TΩ369

3．Encoded theories370

4．Inseparable pairs of sets372

5．Productive and creative sets;reducibility376

6．One-one reducibility;recursive isomorphism384

7．Turing degrees388

8．Post's problem and its solution392

9．Historical and bibliographical remarks398

CHAPTER 9．INTUITIONISTIC FIRST-ORDER LOGIC400

1．Preliminary discussion400

2．Philosophical remark403

3．Constructive meaning of sentences403

4．Constructive interpretations404

5．Intuitionistic tableaux408

6．Kripke's semantics416

7．The Elimination Theorem for intuitionistic tableaux422

8．Intuitionistic propositional calculus433

9．Intuitionistic predicate calculus434

10．Completeness438

11．Translations from classical to intuitionistic logic442

12．The Interpolation Theorem445

13．Some results in classical logic452

14．Historical and bibliographical remarks457

CHAPTER 10．AXIOMATIC SET THEORY459

1．Basic developments459

2．Ordinals468

3．The Axiom of Regularity477

4．Cardinality and the Axiom of Choice487

5．Reflection Principles491

6．The formalization of satisfaction497

7．Absoluteness502

8．Constructible sets509

9．The consistency of AC and GCH516

10．Problems522

11．Historical and bibliographical remarks529

CHAPTER 11．NONSTANDARD ANALYSIS531

1．Enlargements532

2．Zermelo structures and their enlargements536

3．Filters and monads543

4．Topology553

5．Topological groups561

6．The real numbers566

7．A methodological discussion572

8．Historical and bibliographical remarks573

BIBLIOGRAPHY576

GENERAL INDFX584

INDEX OF SYMBOLS595

热门推荐