數理邏輯（第2版） [Mathematical Logic] 下載 mobi epub pdf 電子書 2024

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　　A short digression into model theory will help us to analyze the expressive power of the first-order language， and it will turn out that there are certain deficiencies. For example， the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand， this di~culty can be overcome——-even in the framework of first-order logic——by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
　　Godels incompleteness theorems are presented in connection with several related results (such as Trahtenbrots theorem) which all exemplify the limitatious of machine-oriented proof methods. The notions of computability theory that are relevant to this discussion are given in detail. The concept of computability is made precise by means of the register machine as a

內容簡介

　　What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs?
　　Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godels completeness theorem， which shows that the consequence relation coincides with formal provability： By means of a calculus consisting of simple formal inference rules， one can obtain all consequences of a given axiom system (and in particular， imitate all mathematical proofs)

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目錄

Preface
PART A
ⅠIntroduction
1.An Example from Group Theory
2.An Example from the Theory of Equivalence Relations
3.A Preliminary Analysis
4.Preview
Ⅱ Syntax of First-Order Languages
1.Alphabets
2.The Alphabet of a First-Order Language
3.Terms and Formulas in First-Order Languages
4.Induction in the Calculus of Terms and in the Calculus of Formulas
5.Free Variables and Sentences
Ⅲ Semantics of First-Order Languages
1.Structures and Interpretations
2.Standardization of Connectives
3.The Satisfaction Relation
4.The Consequence Relation
5.Two Lemmas on the Satisfaction Relation
6.Some simple formalizations
7.Some remarks on Formalizability
8.Substitution
Ⅳ A Sequent Calculus
1．Sequent Rules
2．Structural Rules and Connective Rules
3．Derivable Connective Rules
4．Quantifier and Equality Rules
5．Further Derivable Rules and Sequents
6．Summary and Example
7．Consistency
ⅤThe Completeness Theorem
1．Henkin’S Theorem．
2． Satisfiability of Consistent Sets of Formulas（the Countable Casel
3． Satisfiability of Consistent Sets of Formulas（the General Case）
4．The Completeness Theorem
Ⅵ The LSwenheim-Skolem and the Compactness Theorem
1．The L6wenheim-Skolem Theorem．
2．The Compactness Theorem
3．Elementary Classes
4．Elementarily Equivalent Structures
Ⅶ The Scope of First-Order Logic
1．The Notion of Formal Proof
2．Mathematics Within the Framework of Fimt—Order Logic
3．The Zermelo-Fraenkel Axioms for Set Theory．
4．Set Theory as a Basis for Mathematics
Ⅷ Syntactic Interpretations and Normal Forms
1．Term-Reduced Formulas and Relational Symbol Sets
2．Syntactic Interpretations
3．Extensions by Definitions
4．Normal Forms
PART B
Ⅸ Extensions of First-order logic
Ⅹ Limitations of the Formal Method
Ⅺ Free Models and Logic Programming
Ⅻ An Algebraic Characterization of Elementary Equivalence
ⅩⅢ Lindstrom’s Theorems
References
Symbol Index
Subject Index

前言/序言

數理邏輯（第2版） [Mathematical Logic] 下載 mobi epub pdf txt 電子書 格式

評分☆☆☆☆☆

用數學的方法研究邏輯的係統思想一般追溯到萊布尼茨，他認為經典的傳統邏輯必須改造和發展，使之更為精確和便於演算。後人基本是沿著萊布尼茨的思想進行工作的。

評分☆☆☆☆☆

書很不錯，是數理邏輯的經典之作！

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還沒有看，都是經典教材啊

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書很不錯，是數理邏輯的經典之作！

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目錄

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還不錯吧~還不錯啊~~~

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此書不錯

評分☆☆☆☆☆

2書中的推演係統是矢列演算。通過學習以及與公理係統和自然推演係統的對比，可以更有助於整體的提高。

評分☆☆☆☆☆

邏輯是探索、闡述和確立有效推理原則的學科，最早由古希臘學者亞裏士多德創建的。用數學的方法研究關於推理、證明等問題的學科就叫做數理邏輯。也叫做符號邏輯。

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