At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include:

• the representation of mathematical statements by formulas in a formal language;
• the interpretation of formulas as true or false in a mathematical structure;
• logical consequence of one formula from others;
• formal proof;
• the soundness and completeness theorems connecting logical consequence and formal proof;...