Re: A possible structure isomorphic to reality

```>
> 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 be something wrong in your theorem. My friend
> found the error. Your theorem page 12 is wrong, and the error is page
> 13 in he last bullet paragraph, when you do the negation induction
> step for your lemma. When you say: "Since it is not the case that A l=
> ψ(Fi (b)), it is not the case that Aj l= ψ(Fi (b)(j)) by induction."
> This will be true for *some* j, not for an arbitrary j. If you negate
> "for all j Aj l= ψ(Fi (b)(j)) , it means that there is a j such that
> it is not the case that Aj l= ψ(Fi (b)(j)). After that your j is no
> more arbitrary.

It took me a while to understand what you're saying but indeed I see
the error of my proof at this point.
I'm going to try to prove it in a different way but my hope is quite
limited.

Although I have nothing to show for my efforts, I do feel like I
learned a bit along the way.  Thanks for your feedback.

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