Robbins Algebra

Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom

 !(!(x v y) v !(x v !y))=x,

where !x denotes NOT and x v y denotes OR, imply those for a Boolean algebra. The conjecture was finally proven using a computer (McCune 1997).

See also

Boolean Algebra, Huntington Axiom, Robbins Conjecture, Robbins Axiom, Winkler Conditions

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Fitelson, B. "Using Mathematica to Understand the Computer Proof of the Robbins Conjecture." Mathematica in Educ. Res. 7, 17-26, 1998. Fitelson, B. "Proof of the Robbins Conjecture.", E. V. "New Sets of Independent Postulates for the Algebra of Logic, with Special Reference to Whitehead and Russell's Principia Mathematica." Trans. Amer. Math. Soc. 35, 274-304, 1933a.Huntington, E. V. "Boolean Algebra. A Correction." Trans. Amer. Math. Soc. 35, 557-558, 1933b.Kolata, G. "Computer Math Proof Shows Reasoning Power." New York Times, Dec. 10, 1996.McCune, W. "Solution of the Robbins Problem." J. Automat. Reason. 19, 263-276, 1997.McCune, W. "Robbins Algebras are Boolean.", E. "Automated Reasoning."

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Robbins Algebra

Cite this as:

Weisstein, Eric W. "Robbins Algebra." From MathWorld--A Wolfram Web Resource.

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