Robbins Algebra
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).
Fitelson, B. "Using Mathematica to Understand the Computer
Proof of the Robbins Conjecture." Mathematica in Educ. Res. 7,
17-26, 1998. http://library.wolfram.com/infocenter/Articles/1475/.
Fitelson, B. "Proof of the Robbins Conjecture." http://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." http://www.cs.unm.edu/~mccune/papers/robbins/.
Nelson, E. "Automated Reasoning." http://www.math.princeton.edu/~nelson/ar.html.
Weisstein, Eric W. "Robbins Algebra." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/RobbinsAlgebra.html
Contact the MathWorld Team
170141183460469231731687303715884105727