> > 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. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.