There is evidently a weaker version of the embedding concept.
(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."

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