A Mathematical Introduction to Logic

by Herbert B. Enderton

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I have been constructing an author's commentary on what is in the book, intended to help users of the book.
Here is a link to the website for the author's logic course based on the book.

Second edition.   A second edition was published in January 2001.   The publisher is Academic Press, which formerly belonged to Harcourt, but is now part of Elsevier Science.   Click here to request an examination copy.

Click here for the Table of Contents to the second edition.   Click here to see the cover to the second edition, in pdf format.   There is a review of the second edition, by Natasha Dobrinen, in The Bulletin of Symbolic Logic, vol. 9 no. 3, pp. 406-407, with some advice on using the book in a course.   A Postscript file for the review is accessible from this link.

The list price of the book keeps changing; it recently was $107.00.   Click here to connect to the Academic Press catalog entry for the book.   Click here for the Amazon.com listing for the book (recently $85.60).   Click here for the Amazon.co.uk listing for the book.  

Like the first edition, this textbook introduces the mathematics student to the concepts of "proof, truth, and computability."   Major goals of the book include:

• The completeness theorem for first-order logic, which shows that the concept of provability (from axioms) can be completely nailed down.
• The Gödel incompleteness theorem, which shows that there is an inherent gap between what is true (about the whole numbers, for example) and what can be proved in an axiomatic system.
• The unsolvability of the halting probem, which shows that computers can't do everything.

In addition to "local" improvements, the second edition has been changed in the following three ways:

• Accessibility.   I have tried to make the material more accessible to the typical undergraduate student.   In the main development, I have avoided taking for granted information or insights that might be unavailable to a junior-level mathematics student.
• Flexibility.   For the instructor who wants to fit the book to his or her course, the organization has been made more flexible.   Footnotes at the beginning of many of the sections indicate optional paths the instructor -- or the independent reader -- might choose to take.
• CS friendliness.   Theoretical computer science has influenced logic in recent years, and some of that influence is reflected in this edition.   Issues of computability are taken more seriously.   Some material on finite models has been incorporated into the text.

Errata.   Click here for the Errata to the first edition.   Click here for the Errata to the second edition.

Translations.   A Spanish translation of the second edition, Una Introducción Matemática a la Lógica, translated by Professor José Alfredo Amor, has recently been published by Universidad Nacional Autónoma de México.   Information on the book is available from this website; it may be necessary first to select Instituto de Investigaciones Filosóficas and then to hunt for the book.   (In 1987 UNAM had published a Spanish translation of the first edition.)  
A Chinese translation of the second edition was published in 2006 by the Posts & Telecom Press (click on English if you don't read Chinese).   There is more here.   And here is the entry from TuringBook, and the entry from T-Bookshop.  
A Farsi translation of the first edition was published in Tehran by Markaz Nashr Daneshgahi.   I recently received a copy, courtesy of Dr. Saeed Salehi, of the University of Tabriz.

Click here for information on my set theory book, Elements of Set Theory.