info prev up next book cdrom email home

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.


McCune, W. ``Robbins Algebras are Boolean.''

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.

© 1996-9 Eric W. Weisstein