The Transfer Principle
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.
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