Permanence, Comprehensiveness, Saturation

  • Robert Goldblatt
Part of the Graduate Texts in Mathematics book series (GTM, volume 188)


Nonstandard analysis introduces a brave new world of mathematical entities. It also has a number of distinctive structural features and principles of reasoning that can be used to explore this world. Already in the context of subsets of *ℝ we have examined several of these principles: permanence, internal induction, overflow, underflow, saturation. Now we will see that in the context of a universe embedding U → U’ they occur in a much more powerful form, since they apply to properties that may refer to any internal entities in U’. We assume from now on that we are dealing with such an embedding for which *ℕ - ℕ ≠ Ø.


Nonempty Intersection Nonstandard Analysis Internal Function General Topological Space Internal Induction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Robert Goldblatt
    • 1
  1. 1.School of Mathematical and Computing SciencesVictoria UniversityWellingtonNew Zealand

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