There is evidently a weaker version of the embedding concept. http://en.wikipedia.org/wiki/Embedding#Universal_algebra_and_model_theory (No references as far as I can tell for this definition)
I am looking at this definition and the flaw in my proof on page 13 and, while I will have to study it further, preliminarily, it appears that this weakened concept of embedding will work. That is to say that the theorem on page 12 will be correct if I simply remove the word elementary. The Wiki article is somewhat dubious in lacking references to this weakened version of embedding. I don't see this in Chang and Kiesler (so far). The definition given seems to, intuitively, say that A is embedded in B via h if h is 1-1, h preserves the interpretation of function symbols (I'm not sure how else to state that yet), and h preserves the truth of relations. The last bit is significantly weaker than preserving the truth of all formulas. In fact, I never needed the embedding to be "elementary." -- 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.