First Order Mathematical Logic

Attractive and wellwritten introduction. — Journal of Symbolic Logic The logic that mathematicians use to prove their theorems is itself a part of mathematics in the same way that algebra analysis and geometry are parts of mathematics. This attractive and wellwritten introduction to mathematical logic is aimed primarily at undergraduates with some background in collegelevel mathematics however little or no acquaintance with abstract mathematics is needed. Divided into three chapters the book begins with a brief encounter of naïve set theory and logic for the beginner and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two the predicate calculus is developed as a formal axiomatic theory. The statement calculus presented as a part of the predicate calculus is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again and a smoothrunning technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to firstorder theories i.e. mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency completeness independence categoricity and decidability are discussed The predicate calculus is proved to be complete. The book concludes with an outline of Godels incompleteness theorem. Ideal for a onesemester course this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises with selected answers help students test their grasp of the material. For any student of mathematics logic or the interrelationship of the two this book represents a thoughtprovoking introduction to the logical underpinnings of mathematical theory. An excellent text. — Mathematical Reviews