Logic of mathematics

the long version

Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: Godel's theorems of completeness and incompleteness, the independence of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and Matiyasevich's theorem on diophantine formulas. Logic of Mathematics also features full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types; clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Lowenheim constructions and other topics; and carefully chosen exercises for each chapter, plus helpful solution hints.