[FOM] Nonstandard Analysis and the Transfer Principle

Robert Lubarsky Lubarsky.Robert at comcast.net
Sun Dec 23 11:34:37 EST 2012

Sam, your question sounds interesting, but I for one do not understand it.
What is a "classic" nonstandard system? I have a sense of proof-theoretic
strength of an axiom system, but I don't think that's what you mean by
"first-order strength" here. So what does that mean? Are you thinking only
relative to the standard reals, or do you want to relativize the question to
systems non-standard relative to some base system, which could itself be

Bob Lubarsky

-----Original Message-----
From: fom-bounces at cs.nyu.edu [mailto:fom-bounces at cs.nyu.edu] On Behalf Of
Sam Sanders
Sent: Monday, December 17, 2012 7:23 AM
To: Foundations of Mathematics
Subject: [FOM] Nonstandard Analysis and the Transfer Principle

Dear members of the FOM,

One of the ways to obtain a nonstandard extension of the real numbers is via
the well-known ultrafilter construction.  The transfer principle is then a
consequence of Los's Theorem.  However, weak nonstandard systems do not
necessarily satisfy the transfer principle.  

I was wondering how strong a (classic) nonstandard system can be (in terms
of first-order strength) without proving the transfer principle?  Examples
are welcome.  


Sam Sanders
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