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Paper   IPM / M / 123
School of Mathematics
  Title:   Internal approach to external sets and universes: part 2, external universe over the universe of bounded set theory
1.  V. Kanovei
2.  M. Reeken
  Status:   Published
  Journal: Studia Logica
  Vol.:  55
  Year:  1995
  Pages:   347-376
  Supported by:  IPM
In this article we show how the universe of BST, bounded set theory (a modification of IST which is, briefly, a theory for the family of those sets in IST which are members of standard sets) can be enlarged by definable subclasses of sets (which are not necessarily sets in internal theories like BST or IST) so that Separation and Replacement are true in the enlargement for all formulas, including those in which the standardness predicate may occur.
    Thus BST 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.

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