Abstract

In this paper we introduce a collection of isols having some interesting properties. Imagine a collection W of regressive isols with the following features: u, v ϵ W implies that u ⩽ v or v ⩽ u, u ⩽ v and v ϵ W imply u ϵ W, W contains ℕ = {0,1,2,…} and some infinite isols, and u eϵ W, u infinite, and u + v regressive imply u + v ϵ W. That such a collection W exists is proved in our paper. It has many nice features. It also satisfies u, v ϵ W, u ⩽ v and u infinite imply v ⩽ g for some recursive combinatorial function g, and each u ϵ W is hereditarily odd-even and is hereditarily recursively strongly torre. The collection W that we obtain may be characterized in terms of a semiring of isols D introduced by J. C. E. Dekker in [5]. We will show that W = D, where c is an infinite regressive isol that is called completely torre