Is there any first order formula true in only one of R and R*? I would think that if the answer is NO then R < R*. What I'm exploring is the connection of < to [=], with the statement that < implies [=].
Are there any other comparitive relations besides elementary embedding that would fit with what I'm trying to do? What I'm trying to do is one major "leg" of my paper: there is a "superstructure" to all structures. What super means could be any comparitive relation. But what relation is 'good'? On Dec 9, 8:12 am, Bruno Marchal <[email protected]> wrote: > On 09 Dec 2010, at 05:12, Brian Tenneson wrote: > > > > > On Dec 5, 12:02 pm, Bruno Marchal <[email protected]> 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 > > > > > -- > > You received this message because you are subscribed to the Google > > Groups "Everything List" group. > > To post to this group, send email to [email protected]. > > To unsubscribe from this group, send email to > > [email protected] > > . > > For more options, visit this group > > athttp://groups.google.com/group/everything-list?hl=en > > . > > http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
