Finite satisfiability
Statement of Compactness theorem
Proof :
Godel Numbering
Construction of \Delta from \Sigma
Proving that \Delta is satisfiable. 
Lemma : Given \Sigma is FS. Then for any formula \alpha 
       \Sigma \cup \{ \alpha \} is satisfiable OR 
       \Sigma \cup \{ \neg \alpha \} is satisfiable.
Proof of this lemma is remaining.