ABSTRACT
When one learn elementary algebra such as group theory or linear algebra they are introduced to isomorphism as the main classification tool for classifying structures. Combinatorial group was generated by algorithmic considerations such as the word problem of M. Dehn, and yet these considerations have provided an engine for new group theory. The point is that pure existence proofs often simply do not provide enough structure theory to enable the construction of algorithms. The natural guess for a degree for an isomorphism type would be the least degree of any presentation in that type. A structure closely related to orderings is that of Boolean Algebras. While it is possible to prove things directly, it is nice to extract results for Boolean algebras from results for linear orderings via the following technical device.
