Hereditarily Odd–Even and combinatorial isols
Joseph Barback · Pacific Journal of Mathematics · 2002
In this paper we study some of the arithmetic structure that is found in a special kind of semi-ring in the isols.These are the semi-rings [D(Y ), +, •] that were introduced by J.C.E.Dekker, and that were later shown by E. Ellentuck to model the true universal recursive statements of arithmetic when Y is a regressive isol and is hyper-torre (= hereditarily odd-even = HOE).When Y is regressive and HOE, we further reflect on the structure of D(Y ).In addition, a new variety of regressive isol is introduced, called combinatorial.When Y is such an isol, then it is also HOE, and more, and the arithmetic of D(Y ) is shown to have a richer structure.