Review of Classical Mathematical Logic: The Semantic Foundations of Logic, by Richard L. Epstein, With contributions by Leslaw W. Szczerba

Abstract

The main purpose of the book is a detailed exposition of methods used in semantical and deductive analysis of ordinary mathematical reasoning by means of classical mathematical logic. The book contains both a statement of modern mathematical logic and many its applications in various fields of mathematics. Introduction gives a brief review of the trends in mathematics in the 19th century which have resulted in a renewed interest in formal logic and its rapid development in the 20th century. Chapters I–XI contain a rather detailed exposition of basic facts in modern mathematical logic including classical propositional and predicate logics, their semantics and axiomatizations. Chapters XII–XVII present applications of mathematical logic to mathematics. In this connection formalizations of group theory, linear orderings, arithmetic of natural numbers, integers, rationals, and real numbers are considered. First-order and second-order arithmetic theories are discussed. Chapters XVIII and XIX written in collaboration with Lesław Szczerba give...