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The hyperreal numbers are constructed by any free ultrafilter. We know that we can't exhibit a concrete example of a free ultrafilter on natural numbers (see here). Is it possible to give a canonical hyperreal numbers also if it is not possibile to give explicitly a free ultrafilter?

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  • $\begingroup$ What does it mean for a number to be "canonical" here? $\endgroup$ – Hurkyl Aug 17 '18 at 14:52
  • $\begingroup$ ... and what is wrong with the 'obvious' response of "You can give a hyperreal number (in any of this family of models) by giving a sequence of real numbers". $\endgroup$ – Hurkyl Aug 17 '18 at 14:58
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    $\begingroup$ See here and here. $\endgroup$ – Michael Greinecker Aug 17 '18 at 15:27
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    $\begingroup$ When I say canonical I mean the possibility to choice one of the isomorphic contructions of hyperreals $\endgroup$ – asv Aug 17 '18 at 15:36

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