This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraisse's characterization of elementary equivalence, Lindstrom's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

本书是“逻辑与形而上学教科书系列”中的一本。书中从零起点开始，介绍了集合论基本知识，命题逻辑、一阶逻辑的语法和语义，哥德尔完全性定理，递归论基本知识，简化版本的自然数模型，哥德尔不完全性定理等内容。 本书尤其面向对数学基础感兴趣的的读者。相对于其他数理逻辑教材，本书更强调逻辑与元数学的联系，更多地介绍语义部分，强调语法语义的统一。书中，除了对各个知识点本身的讲解，还介绍了它们的直观和思想背景。 本书适合作为数理逻辑系列课程的导论，并为后继课程做准备。为此，在最后一章中简单介绍了数理逻辑当代研究成果及其与本书内容的联系。希望读者掌握了本导论的内容之后有意于继续学习更深、更专门、更有意思的内容。 书中所含习题能使读者通过练习得到必要的训练，并自我检验对有关内容的理解。

本书前六章是集合论的基本内容。第一章集合的基本概念，包括子集和幂集、集合的运、卡氏集和集合族等；第二章映射，映射是集合论中和集合同样重要的基本概念；第三章关系，主要讨论两种重要的二元关系——等价关系和偏序关系；第四章基数，第五章序数，第六章选择公理，这三部分是集合论中最为深刻的内容，从概念的理解到定理的证明都有一定的难度。 本书后三章是一些特殊的内容。第七章简单介绍在现代逻辑中有广泛应用的两

The Handbook of Mathematical Logic is an attempt to share with the entire mathematical community some modern developments in logic. We have selected from the wealth of topics available some of those which deal with the basic concerns of the subject, or are particularly important for applications to other parts of mathematics, or both. Mathematical logic is traditionally divided into four parts: model theory, set theory, recursion theory and proof theory. We have followed this division, for lack of a better one, in arranging this book. It made the placement of chapters where there is interaction of several parts of logic a difficult matter, so the division should be taken with a grain of salt. Each of the four parts begins with a short guide to the chapters that follow. The first chapter or two in each part are introductory in scope. More advanced chapters follow, as do chapters on applied or applicable parts of mathemat- ical logic. Each chapter is definitely written for someone who is not a specialist in the field in question. On the other hand, each chapter has its own intended audience which varies from chapter to chapter. In particular, there are some chapters which are not written for the general mathematician, but rather are aimed at logicians in one field by logicians in another. We hope that many mathematicians will pick up this book out of idle curiosity and leaf through it to get a feeling for what is going on in another part of mathematics. It is hard to imagine a mathematician who could spend ten minutes doing this without wanting to pursue a few chapters, and the introductory sections of others, in some detail. It is an opportunity that hasn’t existed before and is the reason for the Handbook.

本书是数理逻辑方面的经典教材。书中涵盖了命题逻辑、一阶逻辑、不可判定性以及二阶逻辑等方面的内容，并且包含本书是数理逻辑方面的经典教材。书中涵盖了命题逻辑、一阶逻辑、不可判定性以及二阶逻辑等方面的内容，并且包含了与计算机科学有关的主题，如有限模型。本书特点是：内容可读性强；组织结构更灵活，授课教师可根据教学需要节选本书的内容；反映了近几年来理论计算机科学对逻辑学产生的影响；包含较多的示例和说明。本书适合作为计算机及相关专业本科生和研究生数理逻辑课程的教材。. 本书是数理逻辑方面的经典教材，以可读性强而著称，在美国大学中采用率极高，麻省理工学院、加州大学伯克利分校、哥伦比亚大学、康奈尔大学等众多名校均用它作为教材。本版章节组织更加灵活，增加了与计算机科学相关的主题(比如有限模型)，还增加了一些示例和阐释文字，更适合本科生和研究生数理逻辑课程使用。.