[FOM] Smooth Infinitesimal Analysis

Alasdair Urquhart urquhart at cs.toronto.edu
Thu Jul 31 13:52:32 EDT 2003

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.

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