G are a subset of the generators> > for H, so that H _is_ an extension of G:> > > > I have seen it said> > > > <a href="http://en.wikipedia.org/wiki/Free_group#Universal_property>">http://en.wikipedia.org/wiki/Free_group#Universal_property></a> > > > that any two free groups have the same first-order theory...Either it is trivially true that whenever G is a subgroup of H, H is an elementary extension of G, or I am confused about wh