Non-Archimedean extensive measurement with incomparability

Standard theories of extensive measurement require that all objects to be measured are comparable, and that no object is infinitely or infinitesimally greater than another. The present paper develops a theory that leaves room for infinite and infinitesimal differences, as well as incomparable objects. Our result is analogous to the standard representation and uniqueness theorem of extensive measurement, and only simple and familiar mathematical concepts are assumed.

► Standard extensive measurement excludes incomparability and infinite differences.
► We develop a theory allowing for infinite differences and incomparable objects.
► The result is analogous to the standard theorems of extensive measurement.