@article { Gutman20011225,
  author = "Gutman A.E. and Ryabko D.B.",
  title = "Completeness criterion for the nonstandard hull of a normed space in a Boolean-valued universe",
  journal = "Doklady Math.",
  year = "2002",
  volume = "65",
  number = "3",
  pages = "337--338",
  annote = "In this article, we extend some results of infinitesimal analysis on normed spaces and the field of reals to the functional representation of a Boolean-valued universe. In particular, we prove equivalence of the following three conditions for an arbitrary polyverse over $Q$: a point $q\in Q$ is not $\sigma$-isolated; the stalk of the polyverse at $q$ is countably saturated; and the nonstandard hull of every normed space in the stalk of the polyverse at $q$ is complete."
}