FOM: HF on infinitesimals (was: ReplyToDavis)
David Ross
ross at math.hawaii.edu
Tue Nov 11 09:26:26 EST 1997
Though I am a regular user of nonstandard methods, I tend to agree with
HF that their applicability to fom is likely to not be great. However,
the question:
> But can one get a "preferred" one [NS model]?
...reminds me of an interesting foundational point, namely that a
'false' result of Cauchy about convergence of continuous functions can be
rendered 'true' provided we interpret his notion of 'infinitesimal' as the
equivalence class of a sequence <s_n> in an ultraproduct of R w/r to an
ultrafilter which is a p-point.
- David Ross
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