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In the theorem statement there is no constraints on the sequence of terms t_i,j. Either the specification is missing, saying what are the terms and if they are of specific shape. Otherwise, because the terms are not said to be different from each other - the theorem is equivalent to a formulation
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van den Dries, Lou; Macintyre, Angus; Marker, David: The elementary theory of restricted analytic fields with exponentiation. Ann. of Math. (2) 140 (1994), no. 1, 183--205
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page does not seem to say anything much more than this page, thus I suggest a merge. But perhaps there is more to the theory than this individual theorem? I don't know ...
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Every universal and model complete theory in a language has definable Skolem functions, which are given by terms in that language on finitely many definable pieces
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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A work of Dale Miller is cited for the first, but what about the other two?
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Section "Statement" is either false or over-complicated.
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I have seen it used in several places. For instance,
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