Robbins algebra

In abstract algebra, a Robbins algebra is an algebra containing a single binary operation ${\displaystyle \lor }$ and a single unary operation ${\displaystyle \neg }$ that satisfy the following axioms:

For all elements a, b, and c:

1. Associativity: ${\displaystyle a\lor \left(b\lor c\right)=\left(a\lor b\right)\lor c}$
2. Commutativity: ${\displaystyle a\lor b=b\lor a}$
3. Robbins equation: ${\displaystyle \neg \left(\neg \left(a\lor b\right)\lor \neg \left(a\lor \neg b\right)\right)=a}$

For many years, it was conjectured, but unproven, that all Robbins algebras are Boolean algebras. This was proved by William McCune in 1997, so the term "Robbins algebra" is now simply a synonym for "Boolean algebra".