As Dekker  suggested, certain fragments of the isols can exhibit an arithmetic rather more resembling that of the natural numbers than the general isols do. One such natural fragment is Barback's “tame models” (cf. ,  and ), whose roots go back to Nerode . In this paper we study another variety of such fragments: the hyper-torre isols introduced by Ellentuck . Let Y denote an infinite isol with D(Y) the collection of all isols A ≤ f∧(Y) for some recursive and combinational unary function f. (Here, as usual, f∧ is the Myhill-Nerode extension of f to the isols).