Ebook: Boolean Algebra

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.