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
Let [=] denote elementarily equivalence

(A) If M1 < M3 and M2 < M3 then M1 [=] M2.

Consequently, one of my theorems must be wrong since all structures
elementarily embedded within U implies all structures are elementarily
equivalent, which is false.

Firstly, is (A) implied by your statement quoted here?
[quote]
If they are all elementary embeddable within it [my structure U], then
they are all
elementary equivalent, given that the truth of first order formula
are
preserved. All mathematical theories would have the same theorems.
So
eventually there has to be something wrong in your theorem. [unquote]

Secondly, I believe I can prove (A) is false, thus restoring
plausibility of my theorem on page 12.  I still need to prove theorem
on page 12 if possible, of course fixing the flaw which might be a
flaw in the way it was stated.  Perhaps I can rescue the main theorem
even if I weaken the theorem on page 12.

However, if (A) is not implied by your remarks then I wouldn't need to
try to prove it false as my proof would be a moot point.
If (A) is implied by your remarks then I will show my proof that (A)
is false.

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