Robbins Algebra
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by lor, and a single unary operation usually denoted by neg. From these axioms, Huntington derived the usual axioms of Boolean algebra. Specifically, what Huntington proved was that if we take lor to interpret Boolean join, neg to interpret Boolean complement and use lor and neg to define Boolean meet and the constants 0 and 1, then the axioms for a Boolean algeb...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In abstract algebra, a Robbins algebra is an algebra containing a single binary operation, usually denoted by lor, and a single unary operation usually denoted by neg. From these axioms, Huntington derived the usual axioms of Boolean algebra. Specifically, what Huntington proved was that if we take lor to interpret Boolean join, neg to interpret Boolean complement and use lor and neg to define Boolean meet and the constants 0 and 1, then the axioms for a Boolean algebra are satisfied.Very soon thereafter, Herbert Robbins posed the Robbins conjecture, namely that the Huntington axiom could be replaced with Robbins''s axiom, and the result would still be a Boolean algebra in the sense explained in the previous paragraph. Pending verification of the conjecture, the system of Robbins was called "Robbins algebra."
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