[FOM] Question about Conservative Extensions

[Richard Heck]

Hi, all,

I was introducing my students today to model-theoretic proofs that some 
theory is a conservative extension of another, and one of them asked me, 
in effect, when the converse of the usual argument is also true, i.e.: 
If T2 is a conservative extension of T1, can every model of T1 always be 
expanded to a model of T2? I believe the answer must be "no", and that 
models of PA that do not have satisfaction classes would provide one 
counter-example. Is that right? If not, are there other examples? And 
even if so, are there (much) simpler examples?

Thanks,
Richard Heck

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Richard G Heck Jr
Romeo Elton Professor of Natural Theology
Brown University

Check out my book Frege's Theorem:
   http://tinyurl.com/fregestheorem
Visit my website:
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