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The Transfer Principle

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

Abstract

What properties are preserved in passing from ℝ to *ℝ? We have seen a number of examples, and will now consider some more in order to illustrate the powerful logical transfer principle that underlies them. To formulate this principle we will need to develop a precise language in which to describe transferable properties. Ultimately this will allow us to abandon the ultrapower description of *ℝ and ultrafilter calculations, in the same way that the Dedekind completeness principle allows us to abandon the view of real numbers as cuts or equivalence classes of Cauchy sequence of rationals.

Keywords

Relational Structure Free Variable Atomic Formula Transfer Principle Full Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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