[FOM] Nonstandard Analysis and the Transfer Principle

[Sam Sanders]

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.  

Best,

Sam Sanders