Robbins Algebra (original) (raw)
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Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom
where 
denotes NOT and 
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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References
Fitelson, B. "Using Mathematica to Understand the Computer Proof of the Robbins Conjecture." Mathematica in Educ. Res. 7, 17-26, 1998. https://library.wolfram.com/infocenter/Articles/1475/. Fitelson, B. "Proof of the Robbins Conjecture." https://library.wolfram.com/infocenter/MathSource/291/.Huntington, 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." https://www.cs.unm.edu/~mccune/papers/robbins/.Nelson, E. "Automated Reasoning." https://web.math.princeton.edu/~nelson/ar.html.
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Cite this as:
Weisstein, Eric W. "Robbins Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RobbinsAlgebra.html