# Borel sets used in Model Theory

In Lemma 4.4.13 (page 161) of D.Marker- Model Theory book it is proved that $D(F,T)$ (the set of all possible F-diagrams of models of T) is a Borel set.

Can someone explain to me the proof given a little bit more detailed?

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Is there a specific part you're having trouble with, or is it the entire proof? – tomasz Nov 22 '12 at 16:07
I´m a little bit confused about the sets that he sais are Borel, like the $E_1$, $E_2$ etc. Also when he proved that $D \subseteq D(F,T)$. – sanluc Nov 27 '12 at 0:34