[FOM] links between nonstandard analysis and formal logic, and set theory

[Jeremy Avigad]

Dana Scott asks:

> What work in Reverse Mathematics has been done in
> connection with Nonstandard Analysis?

I've shown that interesting portions of nonstandard analysis can be 
carried out in conservative extensions of primitive recursive 
arithmetic, and even weaker theories:

   Weak theories of nonstandard arithmetic and analysis
   in Stephen Simpson, editor, *Reverse Mathematics 2001*,
   A K Peters, 2005, pages 19-46

It's available on my web page,

   http://www.andrew.cmu.edu/user/avigad

under "Research". The introduction mentions related work by a number of 
people, most notably Chuaqui, Sommer, Suppes, and Tanaka. The results 
are also described, briefly, in a survey on forcing in proof theory that 
appears on my web page under "Surveys."

Jeremy Avigad