數理邏輯(第2版) [Mathematical Logic]

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


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圖書介紹

齣版社: 世界圖書齣版公司
ISBN:9787506292276
版次:1
商品編碼:10096474
包裝:平裝
外文名稱:Mathematical Logic
開本:24開
齣版時間:2008-05-01
用紙:膠版紙
頁數:289
正文語種:英語


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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

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

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

數理邏輯(第2版) [Mathematical Logic] 下載 mobi epub pdf 電子書
想要找書就要到 圖書大百科
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

用戶評價

評分

邏輯一下子

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包裝完整,物美價廉。

評分

滿減加券一起買的,簡直不能再白菜,開心

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對學習研究專業領域有價值

評分

發展

評分

很好的一本書很好的一本書很好的一本書很好的一本書很好的一本書很好的一本書

評分

利用計算的方法來代替人們思維中的邏輯推理過程,這種想法早在十七世紀就有人提齣過。萊布尼茨就曾經設想過能不能創造一種“通用的科學語言”,可以把推理過程象數學一樣利用公式來進行計算,從而得齣正確的結論。由於當時的社會條件,他的想法並沒有實現。但是它的思想卻是現代數理邏輯部分內容的萌芽,從這個意義上講,萊布尼茨可以說是數理邏輯的先驅。

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Springer的書必屬經典

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體係

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


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