Conditions arising in the study of the Robbins axiom 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
where
denotes OR and denotes NOT, 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." http://www.cs.unm.edu/~mccune/papers/robbins/.Winkler,
S. "Robbins Algebra: Conditions that Make a Near-Boolean Algebra Boolean."
J. Automated Reasoning6, 465-489, 1990.Winkler, S. "Absorption
and Idempotency Criteria for a Problem in Near-Boolean Algebra." J. Algebra153,
414-423, 1992.
denotes OR and 
denotes NOT, 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.
