Cover; Title Page; Copyright Page; Contents; Preface; Chapter I. The Informal Algebra of Classes; Union, intersection and complementation.; The commutative, associative and distributive laws.; Difference and symmetric difference.; Venn diagrams.; Examples I; Chapter II. 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; Chapter III. 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; Chapter IV. 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; Chapter V. 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. 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. 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 three different axiomatizations, and an outline of a fourth system of axioms appears in the examples. The final chapter, on lattices, examines Boolean algebra in the setting of the theory of partial order. Numerous examples appear at the end of each chapter, with full solutions at the end. This elementary treatment by a distinguished mathematician begins with the algebra of classes and proceeds to discussions of several different axiomatizations and Boolean algebra in the setting of the theory of partial order. Numerous examples appear throughout the text, plus full solutions. 1963 edition
