On hyper‐torre isols

Abstract

Key wordsRegressive isol, hyper-torre isol, hereditarily odd-even isol. MSC (2000) 03D50In this paper we present a contribution to a classical result of E. Ellentuck in the theory of regressive isols. E. Ellentuck introduced the concept of a hyper-torre isol, established their existence for regressive isols, and then proved that associated with these isols a special kind of semi-ring of isols is a model of the true universal-recursive statements of arithmetic. This result took on an added significance when it was later shown that for regressive isols, the property of being hyper-torre is equivalent to being hereditarily odd-even. In this paper we present a simplification to the original proof for establishing that equivalence.