Near-boolean algebras I: Combinatorial aspects

An algebra $\textcolor{red}{}\text{=(A; ?, ?, ′, 0, 1)}$ is near-boolean if every two generated subalgebra is a boolean algebra. It is shown that for n ? 4 there is a near-boolean algebra of size n ≡ 4 or 8 (mod 12), that for n ? 16 and n ≡ 4 or 8 (mod 12) there is a near-boolean algebra of size n which is not a boolean algebra, and that the smallest near-boolean algebra which is not a boolean algebra has 16 elements.