A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

数理逻辑是一门非常成熟的学科 相比于其他教材 本书将逻辑与元数学联系在一起 更多地介绍语义部分和强调语法语义的统一

《集合论:对无穷概念的探索》是“逻辑与形而上学教科书系列”中的一本，书中介绍了集合论的基础知识，共有集合与公理，关系与函数，实数的构造，基数，滤、理想与无界闭集，集合的宇宙，可构成集，力迫等9章内容；除了讨论集合论的基本概念，还讨论了可构成集、力迫法等现代内容，同时还讨论了与连续统假设相关的一些哲学问题。

本卷是这本《集合论导引》的开卷，分为三章，是后续两卷的基础。第1章主要是引进集合论的基本公理、基本概念、基本方法，并给出典型的可数集合的例子，包括自然数集合、整数集合、有理数集合以及彻底有限集合等。第2章主要是引进选择公理以及由此建立起来的基数运算律和一些典型组合实例。第3章专门引进实数集合并对它进行系统分析。本卷将建立一系列基本概念，为全书作铺垫。

美国著名逻辑学家斯穆里安这本脍炙人口的通俗逻辑读物，是一个逐步展开、层层深入的逻辑迷题系统。它从古老的逻辑悖论入门，引进200多则趣闻、故事和奇谲的迷题，最后到达有史以来最了不起的逻辑发现（歌德尔不完全性定理）的洞口。阅读这本兼具科学性、知识性、和趣味性的小书，能使您了解基本的逻辑常识，在饶有兴味的解题过程中测验、训练您的思考、推理能力。 目录 第一篇 逻辑戏话 1.白骗一场？ 2.迷题与猴儿弄玄虚 3.君子与小人 4.忘却林中的艾丽丝 第二篇 波西娅匣及其他秘密 5.波西娅匣的秘密 6.克雷格探长案卷录 7.实用指南——怎么躲开狼精及其他 8.逻辑迷题 9.别利尼牌还是切利尼牌？ 第三篇 神怪故事 10.日神岛 11.僵尸岛 12.德拉古拉还活着吗？ 第四篇 逻辑妙物，光奇彩异 13.逻辑与生活 14.如何证明一切？ 15.从悖论到真理 16.歌德尔的发现

This book is a modern introduction to model theory which stresses applications to algebra throughout the text. The first half of the book includes classical material on model construction techniques, type spaces, prime models, saturated models, countable models, and indiscernibles and their applications. The author also includes an introduction to stability theory beginning with Morley's Categoricity Theorem and concentrating on omega-stable theories. One significant aspect of this text is the inclusion of chapters on important topics not covered in other introductory texts, such as omega-stable groups and the geometry of strongly minimal sets. The author then goes on to illustrate how these ingredients are used in Hrushovski's applications to diophantine geometry. David Marker is Professor of Mathematics at the University of Illinois at Chicago. His main area of research involves mathematical logic and model theory, and their applications to algebra and geometry. This book was developed from a series of lectures given by the author at the Mathematical Sciences Research Institute in 1998.

本书从一阶逻辑的语法和语义开始， 介绍了紧致性定理、Lwenheim–Skolem定理、Tarski准则、量词消去、饱和模型、齐次模型、Omega-稳定理论、不可区分序列以及Morley定理等内容。

本书是作者在新加坡国立大学、北京大学和中国科学院大学为本科高年级学生开设的数理逻辑选修课和在新加坡国立大学、中国科学院数学与系统科学研究院为研究生开设的专业课程所写讲义基础上整理出来的结果。本书主要由一阶逻辑的核心内容和有关数的逻辑探索和分析两大部分组成，其中包括完备性、紧致性、同质缩小、型省略等基本定理；有关数的经典理论的完全性和可定义性分析；哥德尔不完全性定理、丘奇不可判定性定理、塔尔斯基自然数标准模型真相不可定义性定理以及巴黎-哈灵顿不完全性定理。

格奥尔格·康托（1845—1918），德国数学家，集合论的创始人。本书是一部数学经典。它记录了一百年前数学领域的一项惊人成就，也是数学和哲学思想史上关于无穷观念的一场革命。康托完全背离了自古希腊以来千余年的数学传统，创立了集合理论，提出了超穷序数和超穷基数理论，第一次使人们相信，自然数集合与有理数集合是可数的，而实数集合是不可数的；也第一次使人们相信，无穷不仅是存在的，无穷还可以比较大小，甚至无穷可以进行超穷的运算。他所创立的无穷理论，不仅直接促使现代集合论的建立，也极大地推进了数理逻辑的发展，而逻辑和现代集合论构成了全部数学的基础。

Explores additional important decidability results in this thoroughly updated new edition Introduces mathematical logic by analyzing foundational questions on proofs and provability in mathematics Highlights the capabilities and limitations of algorithms and proof methods both in mathematics and computer science Examines advanced topics, such as linking logic with computability and automata theory, as well as the unique role first-order logic plays in logical systems This textbook introduces first-order logic and its role in the foundations of mathematics by examining fundamental questions. What is a mathematical proof? How can mathematical proofs be justified? Are there limitations to provability? To what extent can machines carry out mathematical proofs? In answering these questions, this textbook explores the capabilities and limitations of algorithms and proof methods in mathematics and computer science. The chapters are carefully organized, featuring complete proofs and numerous examples throughout. Beginning with motivating examples, the book goes on to present the syntax and semantics of first-order logic. After providing a sequent calculus for this logic, a Henkin-type proof of the completeness theorem is given. These introductory chapters prepare the reader for the advanced topics that follow, such as Gödel's Incompleteness Theorems, Trakhtenbrot's undecidability theorem, Lindström's theorems on the maximality of first-order logic, and results linking logic with automata theory. This new edition features many modernizations, as well as two additional important results: The decidability of Presburger arithmetic, and the decidability of the weak monadic theory of the successor function. Mathematical Logic is ideal for students beginning their studies in logic and the foundations of mathematics. Although the primary audience for this textbook will be graduate students or advanced undergraduates in mathematics or computer science, in fact the book has few formal prerequisites. It demands of the reader only mathematical maturity and experience with basic abstract structures, such as those encountered in discrete mathematics or algebra.

《模型论基础》介绍模型论的基础知识。主要内容有：紧致性定理，省略型定理，内播定理，完全理论与模型完全理论，初等键，越积，模型论力迫法，他和模型等。并附有模型论方法对经典数学应用的一些例子。《模型论基础》可供大学数学专业高年级学生及研究生、数学教师及数学工作者阅读。也可供其他专业有关数理逻辑及理论计算机科学方面的师生及科学工作者参考。

"This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic."--Publisher's website.

Set theory is concerned with the foundation of mathematics. In the original formulations of set theory, there were paradoxes contained in the idea of the "set of all sets". Current standard theory (Zermelo-Fraenkel) avoids these paradoxes by restricting the way sets may be formed by other sets, specifically to disallow the possibility of forming the set of all sets. In the 1930s, Quine proposed a different form of set theory in which the set of all sets - the universal set - is allowed, but other restrictions are placed on these axioms. Since then, the steady interest expressed in these non-standard set theories has been boosted by their relevance to computer science. The second edition still concentrates largely on Quine's New Foundations, reflecting the author's belief that this provides the richest and most mysterious of the various systems dealing with set theories with a universal set. Also included is an expanded and completely revised account of the set theories of Church-Oswald and Mitchell, with descriptions of permutation models and extensions that preserve power sets. Dr Foster here presents the reader with a useful and readable introduction for those interested in this topic, and a reference work for those already involved in this area.

悖论是逻辑学中最光彩夺目的部分，也是最能激发逻辑学家、数学家、哲学家以及普通大众兴趣的话题，它指的是与公认的信念相左的“道理”，或是让人陷入两难、无所适从的命题。它虽然看似荒谬，违反常理，但却似乎论证缜密、无从反驳。 悖论起源很早，如古希腊的“说谎者悖论”、中国的“白马非马”之说。历史上，众多的哲学家、数学家、逻辑学家对悖论进行了奇妙而艰苦的探索，带给他们成功的快乐和失败的苦痛，并且不断推进了人类智慧的进展，引发哲学和数学的革命。悖论之所以存在的深层原因，还在于人类思维深处的矛盾和裂隙，在对悖论漫长的探索过程中，我们不断攀升人类智慧的高度，同时也意识到其局限和不足。 本书是国内迄今最全面系统地介绍悖论问题的著作，作者将从古至今五花八门的悖论分成十二类，详细介绍每一类悖论的历史原型、各种变体、逻辑学家的解决方案、与日常生活的关系,等等。作为国内著名的逻辑学家，作者展示了多年来在这一领域探索的成果，对于国内外相关领域的逻辑学的研究都将有很大的推动。本书第一版出版后获得了北京市第十四届哲学社会科学优秀成果奖二等奖。 本书第二版重新撰写了第十二章，修订了其他章节中的一些问题。本书的普及版《思维魔方：让哲学家和数学家纠结的悖论》也由北京大学出版社同时出版。

This is an extensively revised edition of Mr. Quine's introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.

现代逻辑起源于19与20世纪之交人类对于数学基础问题的思考。其早期发展无疑是对人类理性事业的重大推动。弗雷格概念文字、希尔伯特公理系统、塔斯基真定义、哥德尔完备性与不完备性定理、图灵机对机械可计算的刻画等成果不仅让人类对数学基础有了全新的理解，孕育了现代计算机科学，还促成了分析哲学的崛起，由此深刻地改变了哲学研究的样貌。 此后的数理逻辑越来越陷入高度的技术化与专业化，并渐渐淡出公众、哲学家甚至其他领域数学家的视野。然而，无论是数学基础问题还是一般的哲学问题都仍然呼唤着哲学与逻辑的再度携手。杨睿之*的《作为哲学的数理逻辑/逻辑与形而上学教科书系列》试图将经过演变与发展的数理逻辑与哲学重新介绍给对方，让哲学工作者或爱好者快速正确地理解当代数理逻辑的主要工作，也让逻辑学工作者或学生了解与他们的工作有关的哲学上的关切。

For 30 years, Quine, a dominant figure in logical theory and philosophy of logic, has combined insights in methodology, language, epistemology, and ontology, to blur the boundaries of speculative metaphysics and natural sciences. This revised text contains two new essays with replies from Quine.