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 fu
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 (x(not your: "for all X there is a Y such that (Y is
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 tr
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 wha
On 09 Dec 2010, at 05:12, Brian Tenneson wrote:
On Dec 5, 12:02 pm, Bruno Marchal 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 embedd
On Dec 5, 12:02 pm, Bruno Marchal 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
On 04 Dec 2010, at 18:50, Brian Tenneson wrote:
On Dec 4, 2:52 am, Bruno Marchal 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 i
On Dec 4, 2:52 am, Bruno Marchal 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 s
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 struct
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 substructure
>
> 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 h
Just as a general comment, I think it's important to reiterate the
actual scope of the paper.
One important assumption I assume is that a complete description of
reality is independent of humans and anything carrying human
"baggage." Admittedly, a mathematical structure as defined within the
cont
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 inte
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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