Goodstein R Boolean Algebra 2012 torrent

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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