Introduction to Elementary Mathematical Logic

This lucid, non-intimidating presentation by a Russian scholar introduces the fundamentals of mathematical logic and its principles. Rather than a survey of the entire topic of mathematical logic, it emphasizes the classical logic of propositions and predicates. Applications include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. Accessible to high school students, the treatment also constitutes a valuable review of fundamentals for professionals.
The three-part treatment examines propositional logic, the propositional calculus, and predicate logic, treating each area in considerable detail. Of special interest is a section devoted to the application of the logic of propositions to the analysis and synthesis of digital systems. Each chapter concludes with a set of exercises, and supplements include three appendixes with one proof each, two indexes, and a bibliography.

Author's Preface; Introduction
I. Propositional Logic
  1. Objects and operations
  2. Formulas. Equivalent formulas. Tautologies
  3. Examples of the application of the laws of the logic of propositions in derivations
  4. Normal forms of functions. Minimal forms
  5. Application of the algebra of propositions to the synthesis and analysis of discrete-action networks
II. The Propositional Calculus
  1. The axiomatic method. The construction of formalized languages
  2. Construction of a propositional calculus (alphabet, formulas, derived formulas)
  3. Consistency, independence, and completeness of a system of axioms in the propositional calculus
III. Predicate Logic
  1. Sets. Operations on sets
  2. The inadequacy of propositional logic. Predicates
  3. Operations on predicates. Quantifiers
  4. Formulas of predicate logic. Equivalent formulas. Universally valid formulas
  5. Traditional logic (the logic of one-place predicates)
  6. Predicate logic with equality. Axiomatic construction of mathematical theories in the language of predicate logic with equality
Appendix I. A proof of the duality principle for propositional logic
Appendix II. A proof of the deduction theorem for the propositional calculus
Appendix III. A proof of he completeness theorem for the propositional calculus
Bibliography; Index of Special Symbols; Index