Unifom chains of small transfinite rank

We extend F.Pastjin’s construction of uniform decomposable chains of finite rank to those of rank ‘finite over a limit’ and investigate infinite products and unions of such chains. We derive an extension of Pastjin’s characterisation to uniform decomposable chains of small transfinite rank (less than or equal to ‘omega+omega’). We conclude by indicating how the resulting descriptions can be iterated to chains of rank ‘omega to the omega’, and beyond.