This book covers the central topics of first-order mathematical logic in a way that can reasonably be completed in a single semester. From the core ideas of languages, structures, and deductions we move on to prove the Soundness and Completeness Theorems, the Compactness Theorem, and G¨odel’s First and Second Incompleteness Theorems. There is an introduction to some topics in model theory along the way, but I have tried to keep the text tightly focused.

One choice that I have made in my presentation has been to start right in on the predicate logic, without discussing propositional logic first. I present the material in this way as I believe that it frees up time later in the course to be spent on more abstract and difficult topics. It has been my experience in teaching from preliminary versions of this book that students have responded well to this choice. Students have seen truth tables before, and what is lost in not seeing a discussion of the completeness of the propositional logic is more than compensated for in the extra time for Gödel’s Theorem.