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.

Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods — including classification theory and nonstandard analysis — the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Skolem functions, indiscernibles, ultraproducts, and special models. The final chapters present more advanced topics that feature a combination of several methods. This classic treatment covers most aspects of first-order model theory and many of its applications to algebra and set theory.

本书是一本经典的逻辑教书，第四版已经过全面修订，提高了可读性。全书主要论述了可计算性理论、基础元逻辑及一些高级专题。此书同样适用于没有数学背景知识的学生，不仅包括了中等深度的逻辑教程所讨论的基本专题，如歌德尔不完全性定理等，而且涉及了从图灵的可计算性理论到Ramsey定理的大量选题，因而已成为一个本经典的教科书。该书在每章末尾还增加了习题，并重新组织和改写了某些章，以使各章更加相互独立，增加了教师授课的灵活性，进而扩大了本书的使用范围。 本书适合数学、计算机科学、哲学等专业的学生使用。对于在人工智能、哲学、计算理论、离散结构、数理逻辑等领域进行研究的读者，此书也是大有裨益的。

《哥德尔证明》是第一本既面向学者又面向非专业人士，对哥德尔证明的主要思路和广泛含义作了易读的解释的书。对任何具有逻辑和哲学品味的受过教育的人士来说，它提供了一个深入了解先前无法企及的论题的机会。 在此书的新版中，普利策奖的获奖作者道格拉斯•R·霍夫斯塔特对这一经典著作的原文进行了重新斟酌和更新，澄清了模糊之处，使论述更为清晰，并使行文更具可读性。

书中讨论了“为什么某些用分式定义的序列只产生整数”，“怎样才能让两人通过电话玩扑克，还要保证对手不受欺骗”等许多有趣的数学问题。

《数理逻辑(第2版)》适合作为数学、哲学、计算机科学以及其他学科需要学习数理逻辑课程的本科生和研究生的教材。