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Theories of internal sets

  • Vladimir Kanovei
  • Michael Reeken
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The class ⌷ of all internal sets, or, more exactly, the structure ⌷, is a very important substructure of the nonstandard set universe of HST because it contains many typically nonstandard objects like infinitely large or infinitesimal numbers (see Chapter 2). It will be demonstrated (Theorem 3.1.8) that 〈⌷ ; ∈, st〉 satisfies the axioms of bounded set theory BST a variant of Nelson’s internal set theory IST.

Keywords

Standard Parameter Standard Function Arbitrary Parameter Basic Idealization Nonstandard Analysis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir Kanovei
    • 1
  • Michael Reeken
    • 2
  1. 1.IITP, Institute for Information TransmissionMoscowRussian Federation
  2. 2.Bergische Universität WuppertalFB C MathematikWuppertalGermany

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