Logic of Mathematics: A Modern Course of Classical Logic

A comprehensive introduction to the study of deductive argument, structure and relations of statements found in symbolic logic. Beginning with introductory material that develops the theory of relational structures with a particular emphasis on Boolean algebras, the text goes on to introduce and discuss formulas, the truth relation, theories, models, definability, compactness, ultraproducts, realization, omitting of types, and so on. The second half of the text consists of famous theorems crucial in the development of mathematical logic including Godel's theory, Goodstein's theorem from Peano arithmetic, Cohen's proof of Tarski's theorem on elimination of quantifiers, and the Matiyasevich theorem on diophantine relations.