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我国的讀者近来已越來越多地对数理邏輯发生兴趣了,这是一个很好的現象。它表明了我国大众已經开始重視这門重要的科学;从而将使这門科学在我們祖国的土地上开出光輝灿烂的花朵来。但是一般讀者每每詢問下列一連串問題:数理邏輯是怎样的一門科学?它研究什么?有什么主要內容?学习它时需要什么预备知識?有什么主要参考书?……这些問題如果得不到很好的回答,对数理邏輯的学习将受到不良的影响。本文的目的想介紹数理邏輯的主要內容,部分地回答上述各問題。由于数理邏輯內容的丰富,任何人想在一篇短文內加以介紹,势必掛一漏万。再由于作者水平不够,本文必然会詳略失宜甚至含有严重的錯誤。因此讀者必須用批判的眼光来閱读它,这样才可以不因本文可能出現的錯誤而受到影响。否則本文原来的目的不但沒有达到反而带來了流弊了。数理邏輯簡史数理邏輯的內容是非常丰富的,要介紹它真是不知从何說起。現在我們先从它的发展过程来說起吧。因为一件东西,无論多么复杂,如果能够从它的发展史来看,每每极易得出它的基本特性的。
Chinese readers have recently become more interested in mathematical logic. This is a very good phenomenon. It shows that the masses of our country have begun to pay attention to this important science; thus it will make this science a brilliant flower in the land of our motherland. But the average reader often asks the following series of questions: What kind of science is mathematical logic? What is it studying? What is the main content? What preliminaries are needed to learn it? What are the main references? The answer to the study of mathematical logic will be adversely affected. The purpose of this article is to introduce the main content of mathematical logic and answer some of the above questions in part. Due to the abundance of mathematical logic, anyone wishing to introduce it in a short article is bound to lose a million. Again, due to the insufficient level of the author, this article will inevitably be misunderstood or even contain serious errors. Therefore, the reader must read it with a critical eye, so that he can not be affected by the errors that may appear in this article. Otherwise, the original purpose of this article has not only reached but has brought about the abuse. The content of the mathematical logic in the history of mathematical logic is very rich. To introduce it, I really don’t know where to start. Now we start with its development process. Because of one thing, no matter how complicated, if we can look at its history of development, it is very easy to draw its basic characteristics.