Near-boolean algebras I: Combinatorial aspects

An algebra =(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.