  Based on the class of epsilon numbers, another binary relational <^1 in the
ordinals is introduced. We will see that we can easily describe all the
isomorphisms that are witnesses of <^1. Afterwards we will show that the
isomorphisms witnesses of <^1 are "essentially the same" than the isomorphisms
of the <_1-relation for finite subsets of ordinals that are closed under "the
cover construction". Finally, through our understanding of <^1 we will see how
it is that <_1 induces thinner kappa-club classes of ordinals: Thinner than the
thinnest class of ordinals seen in the article "Carlson's <_1-relation on the
class of additive principal ordinals"; indeed, the thinnest class of ordinals
induced by <_1 that we will obtain in this article will have as it's first
element the Bachmann's ordinal |ID_1|. An independent proof of this last fact
will be provided in a coming article.
