I asked this question at http://math.stackexchange.com but I didn't get any answer there.

In David Marker's Model Theory, there is a exercise said " we can view a countable Henkin construction as a forcing construction ". But in the book the Henkin construction is used to prove the compactness theorem. He didn't prove the completeness theorem.

So my question is can we use forcing method to prove the completeness of first-order logic?

Thank you in advance.

thatlong? Oh dear. Also, you may want to add [forcing] tag to the MSE question. For completeness of the post, here is a link to the MSE post: math.stackexchange.com/questions/261162/… – Asaf Karagila Dec 18 '12 at 8:36