There is evidently a weaker version of the embedding concept.
http://en.wikipedia.org/wiki/Embedding#Universal_algebra_and_model_theory
(No references as far as I can tell for this definition)
I am looking at this definition and the flaw in my proof on page 13
and, while I will have to study it
On 09 Dec 2010, at 20:43, Brian Tenneson wrote:
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 [=].
The elementary embeddings preserve the
Just to be clear on this:
On 09 Dec 2010, at 20:43, Brian Tenneson wrote:
Is there any first order formula true in only one of R and R*?
So yes, there is one: the weak pure archimedian formula AF:
AF: for all x there is a y such that (xy)
(not your: for all X there is a Y such that (Y
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
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
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
On 04 Dec 2010, at 18:50, Brian Tenneson wrote:
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
On 03 Dec 2010, at 18:56, Brian Tenneson wrote:
I'm going to try to concentrate on each issue, one per post. Let me
say again that your feedback is absolutely invaluable to my work.
In an earlier post you say something that implies the following:
Suppose M1, M2, and M3 are mathematical
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
I'm going to try to concentrate on each issue, one per post. Let me
say again that your feedback is absolutely invaluable to my work.
In an earlier post you say something that implies the following:
Suppose M1, M2, and M3 are mathematical structures
Let denote the elementarily embedded relation
On 16 Oct 2010, at 23:45, Brian Tenneson wrote:
If they are all elementary embeddable within it, then they are all
elementary equivalent, given that the truth of first order formula
are
preserved.
How would all structures be elementarily equivalent?
If M1 is an elementarily
If they are all elementary embeddable within it, then they are all
elementary equivalent, given that the truth of first order formula are
preserved.
How would all structures be elementarily equivalent?
All mathematical theories would have the same theorems. So
eventually there has to
On 09 Oct 2010, at 17:02, Brian Tenneson wrote:
I am starting a new thread which begins with some quotes by myself and
to continue the conversation with Bruno.
I figure this is especially of interest because of the references to
Tegmark's works.
From a logician's standpoint, it may be of
I am starting a new thread which begins with some quotes by myself and
to continue the conversation with Bruno.
I figure this is especially of interest because of the references to
Tegmark's works.
From a logician's standpoint, it may be of interest that I show that
there is a structure U
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