A Course on Mathematical Logic

Description

This is a short, distinctive, modern, and motivated introduction to mathematical logic for senior undergraduate and beginning graduate students in mathematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn Gödel’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached like a branch of mathematics. Serious efforts have been made to make the book suitable for the classroom as well as for self-reading. The book does not strive to be a comprehensive encyclopedia of logic. Still, it gives essentially all the basic concepts and results in mathematical logic. The book prepares students to branch out in several areas of mathematics related to foundations and computability such as logic, axiomatic set theory, model theory, recursion theory, and computability. The main prerequisite for this book is the willingness to work at a reasonable level of mathematical rigor and generality. Cover......Page 1 Universitext......Page 2 A Course on Mathematical Logic......Page 4 Contents......Page 7 Preface......Page 9 1 Syntax of First-Order Logic......Page 11 2 Semantics of First-Order Languages......Page 25 3 Propositional Logic......Page 39 4 Proof and Metatheorems in First-Order Logic......Page 55 5 Completeness Theorem and Model Theory......Page 75 6 Recursive Functions and Arithmetization of Theories......Page 92 7 Incompleteness Theorems and Recursion Theory......Page 116 References......Page 144