Great reference, thanks!

I'm investigating a problem I can phrase two ways, given that the 
category of MV-algebras is equivalent to the category of lattice-ordered 
Abelian groups with a distinguished strong unit.
So one way to phrase my question, and I'm guess it has been answered 
before....

Take LOAGDSU to be the set of wffs that define lattice-ordered Abelian 
groups with a distinguished strong unit.  Now consider the collection of 
all models of LOAGDSU.  The question I have to anyone who knows is this: 
How many nonisomophic models can (the completion of) LOAGDSU have?

I might be redundant there if the theory generated by the wffs in 
LOAGDSU is already complete (I haven't looked into that aspect today 
yet).  Either way, for the ease of expression, let's say that my 
question is this: How many nonisomophic models can LOAGDSU have?

Are any of them in an interesting sense non-standard, such as so called 
nonstandard models of arithmetic can give rise to a 'realm' that all 
natural numbers are in and other 'things' are in this realm that are in 
every other way elementarily equivalent to the usual model of (N, +, ., 
<  ), yet these unlimited numbers are larger than every standard natural 
number.  Hyper-natural numbers these are called.  My point is, do 
non-standard models of LOAGDSU exist and what is even standard about 
LOAGDSU that could be pushed into a "non-standard line of thought."

But the main question is how many non-isomorphic models can LOAGDSU have.


In other news, I will try to apply to give a presentation on the 
promising connections between logic, algebra, and the muh in physics at 
this conference:
http://www.mat.unisi.it/~latd2008/

I just need to concoct the best 2 page abstract I can and submit it.  I 
am crossing my fingers.


Back to the point at hand.  Asking how many different models LOAGDSU has 
is in a natural way equivalent to asking how many models MV-algebra 
has.  THat is because of the theorems in chapter 7 of the book 
referenced in my preceding post about their realization that there is a 
deep connection between MV-algebras and those certain l-groups.

When I think of the 'things', denoted with variables, in an MV-algebra I 
think those are elements in the truth set.  Ex/ in Classical Logic, the 
cardinality of the truth set is two.  When I think of the 'things', also 
denoted by letters, in these l-groups, I think of groups (which are 
containers).

However, due to the deep and categorical connection between those two 
systems, and combine that with my suspicion that the universe mentioned 
in Tegmark's paper about the MUH, I then see 'things' in MV-algebras and 
l-groups (with equipment) as -worldlines- of other 'things'.  These 
structures, like MV-algebras, provide some of the laws of Physics as 
they would be under the MUH.


So I guess my next peek will be into what a standard model of the theory 
of MV-algebras is (like) and see if it would be fruitful to investigate 
nonstandard models of the theory of MV-algebras.





Günther Greindl wrote:
> Dear Brian,
>
> have you had a look at Universal logic?
>
> http://en.wikipedia.org/wiki/Universal_logic
>
> Maybe there are points of interest in there for you (the wikipedia 
> article is only a stub, but contains some names to google).
>
> Cheers,
> Günther
>
>   

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