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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What does it mean for a number to be "canonical" here? – Aug 17 '18 at 14:52
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... 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". – Aug 17 '18 at 14:58
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1See here and here. – Michael Greinecker Aug 17 '18 at 15:27
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1When I say canonical I mean the possibility to choice one of the isomorphic contructions of hyperreals – asv Aug 17 '18 at 15:36