Introduction to Mathematical Logic, Third Edition

“Introduction to Mathematical Logic, Third Edition” by Elliott Mendelson is a comprehensive resource published by Springer in 1987. This edition spans 341 pages and is presented in English. It serves as a compact introduction to fundamental topics in mathematical logic, featuring significant updates such as a new section on semantic trees and an expanded chapter on Axiomatic Set Theory. The text emphasizes effective computability, with Turing computability as a central concept, and includes diagrams to illustrate the construction of Turing machines.

Readers will find detailed coverage of recursion theory, including the s-m-n theorem, the recursion theorem, and Rice’s Theorem. The book also introduces new sections on register machines and random access machines, catering to the interests of computer science students. The proofs of the incompleteness theorems are based on the Diagonalization Lemma, and the text discusses Lob’s Theorem in relation to Godel’s Second Theorem. With numerous new examples and updated notation, this edition is suitable for introductory courses in mathematics, philosophy, computer science, and electrical engineering.