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 structures Let < denote the elementarily embedded relation Let [=] denote elementarily equivalence (A) If M1 < M3 and M2 < M3 then M1 [=] M2.

`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 standard notions,`

`like in Robinson analysis.`

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]

I don't think so. I think (A) is false.

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.

Hmm...

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. --You received this message because you are subscribed to the GoogleGroups "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.

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