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).

REFERENCES

 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, 1933

a.Huntington, E. V. "Boolean Algebra. A Correction." Trans. Amer. Math. Soc. 35, 557-558, 1933

b.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.