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incompleteness theorem
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  不完全性定理
     This paper makes simple analysis on Godel First Incompleteness Theorem and Godel Second In- completeness Theorem,thus demonstrates that there are mistakes in the process of proving the two Godel theorems.
     简述了哥德尔第一不完全性定理和哥德尔第二不完全性定理,通过论证证明哥德尔的两个不完全性定理的证明过程有误。
短句来源
     Godel Incompleteness Theorem definitely reveals and proves the ability limit for oneself to master "truth".
     哥德尔不完全性定理明确揭示和证明自己把握“真”的能力限度。
短句来源
     Incompleteness Theorem indicates that any formal system rich enoughis an incomplete theory, in which proof can be verified mechanically.
     不完全性定理表明任何足够丰富的形式系统都是不完全的理论,而有机械的证明验证是对形式系统的基本要求。
短句来源
     After Gdel's the Incompleteness Theorem, more and more paradox resolutions began to penetrate deeply into the realm of language.
     哥德尔提出不完全性定理之后,众多解决悖论的方案开始深入语言的领域。
短句来源
     These can be clearly illustrated by means of our accounts on Gö del's self-reference theorem and the relationship be-tween Tarski's truth theory in formal language and Gö del's incompleteness theorem.
     克里普克就逻辑悖论成因问题提供了一种准确说明,即自我指称与悖论形成没有关系,经典解悖方案中不存在任何对自我指称的限制,这一点可通过哥德尔自指定理,以及塔尔斯基形式语言真理论与哥德尔不完全性定理之间关系的阐释得到明晰显现。
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  “incompleteness theorem”译为未确定词的双语例句
     Outlet of Democracy: Scope of Godel Incompleteness Theorem
     民主的路径:哥德尔不完全性定理的视界
短句来源
     The others problems discussed are nested interval method,Cantor theorem,Cdel incompleteness theorem and Axiom of choice etc.
     同时对区间套法,康托定理,哥德尔定理,选择公理等与之密切相关的一些问题,作了深入讨论并得出创新性结论。
短句来源
     The Prohibition of Self-reference & Substitution Propositions——The Elimination of the Liar Paradox and Discussion of Godel's Incompleteness Theorem
     禁止使用自指代命题——说谎者悖论的排除和哥德尔定理的讨论
短句来源
     On the Mistakes in the Process of Proving Godel Incompleteness Theorem
     哥德尔不完全性定理的证明过程有误
短句来源
     Godel incompleteness theorem 1 and theorem 2, which are significant and have a far reaching influence on modern mathematical logic and postulation method of logic system, are studied in this paper, a non logic discussion on the proof of Godel incompleteness theorems is given, the main idea their proof is explained non logically, and the peculiarity as well as its far reaching impact of the proof methodology of Godel incompleteness theorems are also discussed.
     研究了对现代数理逻辑与形式系统公理化方法有着深远影响及重大意义的Godel不完备性定理 1和定理 2 ,给出了 Godel不完备性定理证明的一种非形式化论述 . 非形式化地阐述了 Godel不完备性定理证明的基本思想 ,论述了 Godel不完备性定理证明在方法论上的特色及其深远影响
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  相似匹配句对
     D theorem.
     A. D提出的结论。
短句来源
     Theorem.
     定理:设Ω(?)
短句来源
     DISCUSSION ABOUT THE G(?)DEL INCOMPLETENESS THEOREM
     Godel不完全性定理及其哲学意义
短句来源
     On the Mistakes in the Process of Proving Godel Incompleteness Theorem
     哥德尔不完全性定理的证明过程有误
短句来源
     2) incompleteness;
     2) 元表征的不完整性;
短句来源
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  incompleteness theorem
Our examples deal with the algorithmic impossibility of deciding whether a given Hamiltonian can be integrated by quadratures and related questions; they lead to a version of G?del's incompleteness theorem within Hamiltonian mechanics.
      
A parallel result gives a version of G?del's first incompleteness theorem within an (axiomatized) theory of gauge fields.
      
Incompleteness theorem of formal theories from programmer's viewpoint
      
The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability.
      
Consistency, Turing Computability and G?del's First Incompleteness Theorem
      
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Godel incompleteness theorem 1 and theorem 2, which are significant and have a far reaching influence on modern mathematical logic and postulation method of logic system, are studied in this paper, a non logic discussion on the proof of Godel incompleteness theorems is given, the main idea their proof is explained non logically, and the peculiarity as well as its far reaching impact of the proof methodology of Godel incompleteness theorems are also discussed.

研究了对现代数理逻辑与形式系统公理化方法有着深远影响及重大意义的Godel不完备性定理 1和定理 2 ,给出了 Godel不完备性定理证明的一种非形式化论述 .非形式化地阐述了 Godel不完备性定理证明的基本思想 ,论述了 Godel不完备性定理证明在方法论上的特色及其深远影响

In this paper, the author queried a few conclusions in [1] , and elaborated different views on several problems, such as relations between non-Euclidean geometry and real space, relations between mathematical logic and thinking, the significance of Godel's second incompleteness theorem, and so on.

本文对文〔1〕的几个论断提出一些疑问 ,并在“非欧几何与现实空间”、“数理逻辑与思维”、“哥德尔不完备性定理的意义”等若干问题上表述了与《数学是什么》一文中不同的观点。

Ⅰ、The paper introduces the notion of undecidability and incompleteness theorem of Godel. Ⅱ,

本文首先介绍了Gdel的不完全性定理和不可判定的概念。其次指出在二阶的标准分析模型M中,普遍存在不可判定的积分公式,如A_6:integral from n=0 to =∞sintdt=1等。第三,本文介绍了物理学Coulomb散射中的通用的数学公式(3,1):integral from ((d~3x/|x|)e~(-iq·x)=4π/|q|~2并证明了A_6和(3,1)的等价性。第四,根据Gdel的不完全性定理和不可判定的概念,本文认为(3,1),或等价地数学公式A_6可以作为物理学中使用的局部的数学公理。

 
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