[FOM] Question about Conservative Extensions

Richard Heck rgheck at brown.edu
Thu Sep 13 12:10:58 EDT 2012

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?

Richard Heck

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

Check out my book Frege's Theorem:
Visit my website:

More information about the FOM mailing list