[FOM] Smooth Infinitesimal Analysis

[Alasdair Urquhart]

Harvey Friedman raised the question of an 
axiomatic formulation of Smooth Infinitesimal
Analysis.  Chapter VII of the monograph by
Moerdijk and Reyes contains an axiomatic version
of smooth analysis.  

I am no expert on Smooth Infinitesimal Analysis, 
but my impression is that it provides a better
model than Robinsonian analysis for certain
intuitive calculations used by physicists.
The drawback of the theory is that the logic
is necessarily non-classical.

By the way, I don't consider the NSA of Nelson's
Internal Set Theory or the Alsatian school to
be essentially different from the Robinsonian
variety.  Just a different formulation.