A model theoretic proof of Feferman's preservation theorem.
David E. Marker · Notre Dame Journal of Formal Logic · 1984
Let I be a countable first-order language containing a binary relation symbol <.If 2ί and 33 are L-structures and 21 c 93, then we say 33 is & faithful extension of 21 if and only if for any a G 2ί and Z?G33if33t=6 (^) is quantifier free, then φ(v) is in Σ. (ii) If φ(Ό) and ψ(ΰ) are in Σ, then φ{ϋ) Λ φ(v) and φ(v) V ψ(v) are in Σ.