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  • G are a subset of the generators&gt; &gt; for H, so that H _is_ an extension of G:&gt; &gt; &gt; &gt; I have seen it said&gt; &gt; &gt; &gt; <a href="http://en.wikipedia.org/wiki/Free_group#Universal_property&gt;">http://en.wikipedia.org/wiki/Free_group#Universal_property&gt;</a> &gt; &gt; &gt; that any two free groups have the same first-order theory...Either it is trivially true that whenever G is a subgroup of H, H is an elementary extension of G, or I am confused about wh
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