FOM: HF on infinitesimals (was: ReplyToDavis)

David Ross ross at
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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