The Winker conditions are sufficient conditions under which a Robbins algebra becomes a Boolean algebra. They arose
in the study of the Robbins axiom and its connection
with Boolean algebra. Winker studied conditions such as idempotence
or existence of a zero, and showed that each of the conditions
where
denotes OR and denotes NOT, known as the first and
second Winker conditions, suffices. A computer proof
demonstrated that every Robbins algebra satisfies
the second Winker condition, from which it follows immediately that all Robbins
algebras are Boolean.
McCune, W. "Robbins Algebras Are Boolean." https://www.cs.unm.edu/~mccune/papers/robbins/.Winker,
S. "Robbins Algebra: Conditions that Make a Near-Boolean Algebra Boolean."
J. Automated Reasoning6, 465-489, 1990.Winker, 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 Winker conditions, suffices. A computer proof
demonstrated that every Robbins algebra satisfies
the second Winker condition, from which it follows immediately that all Robbins
algebras are Boolean.
