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

Jeremy Avigad avigad at cmu.edu
Sun Jan 15 21:15:55 EST 2006

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,


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

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