《Logical Foundations of Mathematics and Computational Complexity》电子书下载

Logical Foundations of Mathematics and Computational Complexitytxt,chm,pdf,epub,mobi下载
作者:Pavel Pudlák
出版社: Springer
副标题: A Gentle Introduction
出版年: 2013-4-23
页数: 695
定价: USD 189.00
装帧: Hardcover
ISBN: 9783319001180

内容简介 · · · · · ·

The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdiscip...

目录 · · · · · ·

1 Mathematician’s World ......................... 1
1.1 Mathematical Structures....................... 2
1.2 Everything Is a Set.......................... 25
1.3 Antinomies of Set Theory ...................... 36
1.4 The Axiomatic Method ....................... 43
1.5 The Necessity of Using Abstract Concepts . . . . . . . . . . . . . 54
· · · · · ·()
1 Mathematician’s World ......................... 1
1.1 Mathematical Structures....................... 2
1.2 Everything Is a Set.......................... 25
1.3 Antinomies of Set Theory ...................... 36
1.4 The Axiomatic Method ....................... 43
1.5 The Necessity of Using Abstract Concepts . . . . . . . . . . . . . 54
Main Points of the Chapter ........................ 64
2 Language,Logic and Computations .................. 65
2.1 The Language of Mathematics.................... 66
2.2 Truth and Models .......................... 80
2.3 Proofs ................................ 92
2.4 Programs and Computations.....................123
2.5 The Lambda Calculus ........................146
Main Points of the Chapter ........................155
3 Set Theory.................................157
3.1 The Axioms of Set Theory......................159
3.2 The Arithmetic of Infinity......................176
3.3 What Is the Largest Number? ....................196
3.4 Controversial Axioms ........................215
3.5 Alternative Set-Theoretical Foundations . . . . . . . . . . . . . . 231
Main Points of the Chapter ........................253
4 Proofs of Impossibility..........................255
4.1 Impossibility Proofs in Geometry and Algebra . . . . . . . . . . . 256
4.2 The Incompleteness Theorems ...................272
4.3 Algorithmically Unsolvable Problems. . . . . . . . . . . . . . . . 300
4.4 Concrete Independence .......................319
4.5 The Independent Sentences of Set Theory. . . . . . . . . . . . . . 340
Main Points of the Chapter ........................364
5 The Complexity of Computations....................365
5.1 What Is Complexity? ........................366
5.2 Randomness, Interaction and Cryptography . . . . . . . . . . . . . 410
5.3 Parallel Computations........................437
5.4 Quantum Computations .......................448
5.5 Descriptional Complexity ......................479
Main Points of the Chapter ........................493
6 Proof Complexity.............................495
6.1 Proof Theory.............................496
6.2 Theories and Complexity Classes..................523
6.3 Propositional Proofs.........................540
6.4 Feasible Incompleteness.......................562
Main Points of the Chapter ........................580
7 Consistency,Truth and Existence....................583
7.1 Consistency and Existence......................584
7.2 The Attributes of Reality ......................609
7.3 Finitism and Physical Reality ....................646
Main Points of the Chapter ........................664
Bibliographical Remarks ...........................667
References .
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