Sufficient conditions for an ordered-ring isomorphism onto a positive subinterval: A lemma for polynomial measurement

This paper discusses a sufficient set of conditions for a structure to be ordered-ring isomorphic to a positive subinterval of the real numbers. It extends our previous results concerning bounded versions of Hölder's Theorem (Falmagne, 1971). The main result can serve as a basic lemma for establishing representation theorems in polynomial conjoint measurement when the empirical sets contain neither large elements nor ones close to the natural zero.