On Wed, Nov 11, 2009 at 10:36 PM, Andrew Salch <asalch@math.jhu.edu> wrote:
I have a question for the category theorists which is unfortunately just an issue about sets and classes that I hope some of you have thought about before, and can help me with: let C be a class, and consider a family of subclasses C_i of C, which are indexed by an index class I. Am I allowed to take the intersection of a family of classes indexed by a class? Is the result a class?
Suppose the class I is described by a first-order formula a(x) and the classes C_i are described by a first-order formula c(x,i), i.e: I = {i | a(i)} C_i = {x | c(x,i)} Then the intersection of the C_i's is a class because it is described as D = {x | forall i, a(i) => c(x,i)} Your condition that the C_i's are contained in a class C is redundant because we may always take C=V, the universe. With kind regards, Andrej [For admin and other information see: http://www.mta.ca/~cat-dist/ ]