Archimedean vector lattices generated by two elements

The class of vector lattices referred to in the title is investigated from the point of view of the free vector lattice on two elements. It is shown that only three of these vector lattices are indecomposable. They are then described. A complete structure theorem for projective vector lattices generated by two elements is proved. The arguments depend throughout on the precise description of the free vector lattice which is established in the first section.