SUO: power classes
All, especially set-theorists,
In formulating axioms the Classification Ontology I have come across a
foundation question about the "power operator". I am following the
small-large approach to foundations as advocated by Adamek, Herrlich and
Strecker in section 0.2 of their book "Abstract and Concrete Categories"
1990, ISBN: 0-471-60922-6, QA169.A3199 1989. The basic concepts are sets,
classes and conglomerates. One axiom is that sets are closed under power;
that is, if A is a set then P(A), the collection of all subsets of A, is
also a set. They seem to indicate that classes are not closed under power,
since they give P(U), the power of the universe, as an example of an
illegitimate conglomerate (legitimate conglomerates correspond to classes; a
conglomerate X is *legitimate* when there is a class Y and a surjection Y ->
X).
So, is it ill-advised to assume that classes are closed under power? What
precisely is the problem here? This question came up when trying to model
the fundamental condition for infomorphisms using fibers in categories.
Robert E. Kent
rekent@ontologos.org