Herbrand基本定理-百科全书文章
Herbrand's Fundamental Theorem - an encyclopedia article
摘要：
Herbrand基本定理用谓词逻辑的方法构造性地刻画了一阶谓词逻辑的可导性。有时它只是所谓的“Herbrand定理”，但较长的名称是可取的，因为还有其他重要的“Herbrand定理”和Herbrand本人称之为“Theorème fondamental”。Bernays [1957]对它的排名如下：“在它的证明论形式中，Herbrand定理可以被看作是谓词逻辑的中心定理。它以一种简洁而恰当的形式表达了谓词逻辑与命题逻辑的关系。海杰努特（Heijenoort，1967）说：“让我简单地说，在结论中，Begriffsschrift（Frege，1879），Löwenheim的论文（1915）和Herbrand论文（1930）的第五章是现代逻辑的三个基石。Herbrand的基本定理出现在他的博士论文[1930年]的第5章-题为Recherches sur la théorie de la démonstration -由Jacques Herbrand（1908-1931）于1929年在巴黎大学提交。赫布兰德基本定理与哥德尔不完备性定理和根岑的Hauptstern定理一起，是现代逻辑中最有影响力的定理之一。由于其复杂性，赫布兰德基本定理在教科书中通常被搞得面目全非。由于我们相信，这个定理还有很多东西需要学习，比许多逻辑学家所知道的要多得多，我们将把重点放在真正的信息及其实际影响上。这需要对赫布兰德的著作进行一定程度的精简，这将通过对实际历史事实的一些评论来补偿。
英文摘要：
Herbrand's Fundamental Theorem provides a constructive characterization of derivability in first-order predicate logic by means of sentential logic. Sometimes it is simply called "Herbrand's Theorem", but the longer name is preferable as there are other important "Herbrand theorems" and Herbrand himself called it "Théorème fondamental". It was ranked by Bernays [1957] as follows: "In its proof-theoretic form, Herbrand's Theorem can be seen as the central theorem of predicate logic. It expresses the relation of predicate logic to propositional logic in a concise and felicitous form." And by Heijenoort [1967]: "Let me say simply, in conclusion, that Begriffsschrift [Frege, 1879], Löwenheim's paper [1915], and Chapter 5 of Herbrand's thesis [1930] are the three cornerstones of modern logic." Herbrand's Fundamental Theorem occurs in Chapter 5 of his PhD thesis [1930] --- entitled Recherches sur la théorie de la démonstration --- submitted by Jacques Herbrand (1908-1931) in 1929 at the University of Paris. Herbrand's Fundamental Theorem is, together with Gödel's incompleteness theorems and Gentzen's Hauptsatz, one of the most influential theorems of modern logic. Because of its complexity, Herbrand's Fundamental Theorem is typically fouled up in textbooks beyond all recognition. As we are convinced that there is still much more to learn for the future from this theorem than many logicians know, we will focus on the true message and its practical impact. This requires a certain amount of streamlining of Herbrand's work, which will be compensated by some remarks on the actual historical facts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
