FOM: Learning to love ACA_0

[Peter Smith]

I've just made a draft paper "Learning to love ACA_0" available at 
www.phil.cam.ac.uk/Smith/Subsystems.pdf (case sensitive address).
The abstract reads

       This paper picks up just one central  theme from Stephen Simpson's 
encyclopedic Subsystems of
       Second-order Arithmetic, concerning the mathematical power of a 
system of arithmetic conventionally
       labeled ACA_0 (though I add a few remarks about a weaker 
arithmetic, RCA_0). I argue that ACA_0
       can be given a rather attractive and stable philosophical 
motivation, and explore Simpson's suggestion
       that this system is indeed genuinely revealing about the 
commitments of applicable real analysis. By
       cutting through the mass of technical detail, I hope to bring into 
sharper focus the philosophical importance
       of the kind of work that Simpson reports.

And the first footnote adds

       This draft paper writes up a talk given at the Philosophy of 
Mathematics Workshop held at Fitzwilliam
       College, Cambridge on 1 June 2002. I am grateful for the 
encouraging reactions of participants, in
       particular Dan Isaacson, Arnold Koslow and Michael Potter. The 
present version is still underworked,
       and it obviously lacks references and additional footnotes; but 
I've got to the stage where I'd very much
      welcome reactions. E-mail: ps218 at cam.ac.uk

So don't expect frontier-breaking stuff: but all comments most 
gratefully received.

Regards to all FOMers

Peter Smith