On 09 Dec 2010, at 05:12, Brian Tenneson wrote:

On Dec 5, 12:02 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:On 04 Dec 2010, at 18:50, Brian Tenneson wrote: That means that R (standard model of the first order theory of the reals + archimedian axiom, without the term "natural number") is not elementary embeddable in R*, given that such an embedding has to preserve all first order formula (purely first order formula, and so without notion like "natural number").I'm a bit confused. Is R < R* or not? I thought there was a fairly natural way to elementarily embed R in R*.

I would say that NOT(R < R*).

`*You* gave me the counter example. The archimedian axiom. You are`

`confusing (like me when I read your draft the first time) an`

`algebraical injective morphism with an elementary embedding. But`

`elementary embedding conserves the truth of all first order formula,`

`and then the archimedian axiom (without natural numbers) is true in R`

`but not in R*.`

`Elementary embeddings are *terribly* conservator, quite unlike`

`algebraical monomorphism or categorical arrows, or Turing emulations.`

Bruno

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