20/05/11 17:39:06 zmgc47N7.net
>>498
つづき
In some sense, the notions of a “set” and of a “bijection of sets” allow one to achieve such “identifications”.
That is to say, the mathematical objects at both higher and lower levels of the ∈-structure constitute examples of the same mathematical notion of a “set”,
so that one may consider “bijections of sets” between those sets without violating the axiom of foundation.
In some sense, the notion of a species may be thought of as a natural extension of this observation.
That is to say,
the notion of a “species” allows one to consider, for instance, speciesisomorphisms between species-objects that occur at different levels of the ∈-structure of the set theory under consideration - i.e., roughly speaking, to “simulate ∈-loops” - without violating the axiom of foundation.
Moreover, typically the sorts of species-objects at diff