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)

內頁插圖

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☆☆☆☆☆

還沒有看，都是經典教材啊

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簡而言之，數理邏輯就是精確化、數學化的形式邏輯。它是現代計算機技術的基礎。新的時代將是數學大發展的時代，而數理邏輯在其中將會起到很關鍵的作用。

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命題演算是研究關於命題如何通過一些邏輯連接詞構成更復雜的命題以及邏輯推理的方法。命題是指具有具體意義的又能判斷它是真還是假的句子。 如果我們把命題看作運算的對象，如同代數中的數字、字母或代數式，而把邏輯連接詞看作運算符號，就象代數中的“加、減、乘、除”那樣，那麼由簡單命題組成復和命題的過程，就可以當作邏輯運算的過程，也就是命題的演算。

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可以

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還行有點貴瞭

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邏輯問題，初步奠定瞭數理邏輯的基礎。

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産生

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可以三年不買衣，不能忍受一日不看書

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書很不錯，是數理邏輯的經典之作！

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