A course on mathematical logic (Q5920368)

The main goal of this book is to give a motivated introduction to mathematical logic for graduated and advanced undergraduate students of logic, set theory, recursion theory and computer science. Its intended audience includes also all mathematicians who are interested in knowing what mathematical logic is dealing with. The book is focused on presenting and proving Gödel's completeness and incompleteness theorems in precise mathematical terms. The first four chapters should make a satisfactory course in mathematical logic for undergraduate students. They deal with the syntax of first-order logic, semantics of first-order languages, propositional logic, and proof and metatheorems in first-order logic, respectively. Chapter 5 treats the completeness theorem and model theory. Some applications of logic to mathematics are also presented. The purpose of Chapter 6 is to study recursive functions and arithmetization of theories. In the last chapter the incompleteness theorems and recursion theory are discussed. All results included in the book are very carefully selected and proved. The author's manner of writing is excellent, which will surely make this book useful to many categories of readers. So, it contributes to the development of this fundamental domain of mathematics.