On Dec 4, 2:52 am, Bruno Marchal <marc...@ulb.ac.be> wrote:

> I just said that if M1 < M2, then M1 [=] M2. This means that M2 needs  
> higher order logical formula to be distinguished from M1.
> Elementary embeddings (<) are a too much strong notion of model  
> theory. It is used in context where we want use non standard notions,  
> like in Robinson analysis.

Doesn't the archemedian property show that R is not elementarily
equivalent to R*?  I mean the following 1st order formula true in only
one of R and R*:
for all X there is a Y such that (Y is a natural number and X<Y)

This is true in R but not in R*.  This would appear to me to be an
example of why R is not [=] to R*.

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