Winkler Conditions

Conditions arising in the study of the Robbins Equation and its connection with Boolean Algebra. Winkler studied Boolean conditions (such as idempotence or existence of a zero) which would make a Robbins Algebra become a Boolean Algebra. Winkler showed that each of the conditions

$$\exists C, \exists D, C+D=C$$

$$\exists C, \exists D, n(C+D)=n(C),$$

known as the first and second Winkler conditions, Suffices. A computer proof demonstrated that every Robbins Algebra satisfies the second Winkler condition, from which it follows immediately that all Robbins Algebras are Boolean.

References

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

Winkler, S. ``Robbins Algebra: Conditions that Make a Near-Boolean Algebra Boolean.'' J. Automated Reasoning 6, 465-489, 1990.

Winkler, S. ``Absorption and Idempotency Criteria for a Problem in Near-Boolean Algebra.'' J. Algebra 153, 414-423, 1992.