Internal approach to external sets and universes

In this article we show how the universe ofBST,bounded set theory (a modification ofIST which is, briefly, a theory for the family of those sets inIST which are members of standard sets) can be enlarged by definable subclasses of sets (which are not necessarily sest in internal theories likeBST orIST) so that Separation and Replacement are true in the enlargement for all formulas, including those in which the standardness predicate may occur.ThusBST is strong enough to incorporate external sets in the internal universe in a way sufficient to develop topics in nonstandard analysis inaccessible in the framework of a purely internal approach, such as Loeb measures.Presented byRobert Goldblatt