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Famous for the number-theoretic first-order statement known as Goodstein's theorem, author R.L. Goodstein was also well known as a distinguished educator. With this text, he offers an elementary treatment that employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. The text begins with an informal introduction to the algebra of classes, exploring union, intersection, and complementation; the commutative, associative, and distributive laws; difference and symmetric difference; and Venn diagrams. Professor Goodstein proceeds to a detailed examination of t. Contents: Preface The Informal Algebra of Classes Union, intersection and complementation The commutative, associative and distributive laws Difference and symmetric difference Venn diagrams Examples I The Self-Dual System of Axioms Standard forms Completeness of the axiom systems Independence of the axioms An algebra of pairs Isomorphism and homomorphism Examples II Boolean Equations Equivalence of the two formalizations Independence of the axioms A bi-operational system of axioms. The general solutions of Boolean equations. Congruence relations Examples III Sentence Logic Sentence logic as a model of Boolean algebra Truth-table completeness Independence of the axioms The third system of axioms The deduction theorem Examples IV Lattices Partially ordered sets Upper and lower bounds Distributive lattices Union and intersection ideals The lattice of union ideals Representation theorems for Boolean algebras Complemented distributive lattices Atoms, minimal and maximal elements Newman algebra. A denumerable Boolean algebra. Examples V Solutions to Examples Bibliography Index