On the Minimality of Tame Models in the Isols

Based on the work of Hirschfeld, it is known that there is a close connection between models for the n°j fragment of arithmetic and homomorphic images of the semiring of recursive functions. This fragment of arithmetic includes most of the familiar results of classical number theory. There is a realization of this fragment in the isols in systems called tame models. In this paper a new proof is given to the following result of Ellentuck and McLaughlin on the minimality of tame models: If two tame models share an infinite element, then the models are equal.