Robbins Algebra

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

$$n(n(x + y) + n(x + n(y))) = x,$$

imply those for a Boolean Algebra. The conjecture was finally proven using a computer (McCune 1997).

References

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.

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

McCune, W. ``Solution of the Robbins Problem.'' J. Automat. Reason. 19, 263-276, 1997.

McCune, W. ``Robbins Algebras are Boolean.'' http://www-unix.mcs.anl.gov/~mccune/papers/robbins/.

Nelson, E. ``Automated Reasoning.'' http://www.math.princeton.edu/~nelson/ar.html.