Introduction to Mathematical Logic (Discrete Mathematics and Its Applications)

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them.
Introduction to Mathematical Logic includes:

propositional logic

first-order logic

first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski

axiomatic set theory

theory of computability
The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

Nearly forty years after it was published (1964), Elliot Mendelson's Introduction to Mathematical Logic still remains the best textbook on the principle topics of this subject...I have used Mendelson's book to teach a one-semester course to advanced undergraduate and graduate students with great success.
- Alan Berger

In my work as a math teacher, researcher, author and journal editor, I often encounter problems with a logical component. When that need arises, my first choice of reference is always this book. It is the most concise and readable introductory text I have ever encountered and it is a rare occasion when I fail to find the background material needed to solve the problem. It is also an excellent source of problems and I have pulled the ideas for many test questions from it over the years.
-Charles Ashbacher

I was sufficiently fortunate to have taken Professor Emeritus Mendelson's famous logic course at Queens College, the City University of New York, just two semesters before his retirement. I was, and continue to be, astonished by Dr. Mendelson's precise yet easy style, and the beautifully efficient organization of the subjects. Everything from the expository prose to the system of notational conventions has been carefully thought through so as to make the book both very substantive and very readable. In my opinion, it's the best introduction to serious mathematical logic currently on the market, and thanks to the genius of its author, it is likely to remain so for a long time. The buyer will not be disappointed.
-Joseph Jay Stern