Extending Henkin's Theorem to Completeness in Marker's Text In Marker's Model Theory, starting on p. 35, he proves the following:
Theorem [Henkin]: If $T$ is finitely satisfiable, then $T$ is satisfiable. 
He also mentions 
Theorem [Goedel]: If $T$ is consistent, then $T$ is satisfiable.
What I am not seeing is how to prove:
Lemma: If $T$ is consistent, then $T$ is finitely satisfiable
without already using Compactness or Completeness. Any ideas? Thanks!
 A: The basic issue is that the completeness theorem and the lemma you state in your question involve the notion of consistency of a theory, which is a proof theoretic notion ($T$ is consistent if there is no proof of a contradiction from $T$), whereas the compactness theorem deals only with (finite) satisfiability, which is a model theoretic notion. If Marker had wanted to prove the completeness theorem in his book, he would have had to introduce a proof system for first-order logic, which would have been irrelevant for the rest of the book (made obsolete, in fact, by the completeness theorem, which says we can replace consistency with satisfiability and syntactic consequence $\vdash$ with semantic consequence $\models$).
In the presence of a proof system for first-order logic, the Henkin proof that Marker gives can be easily adapted to prove the completeness theorem. One place where you can read the details is in Chang and Keisler's Model Theory (recently reprinted by Dover) - C&K set out a proof system in Section 1.3 (pp. 24-25) and prove completeness via the Henkin method in Section 2.1.
Here are two related math overflow questions with excellent answers (including one from Marker himself).
In model theory, does compactness easily imply completeness?
Completeness vs Compactness in logic
