Class 16 :  DT, Soundness, consistency

Completion of proof of deduction theorem 
Example proof of \derives (\neg \neg \alpha) --> \alpha

Soundness theoreom : \Sigma \derives \alpha \implies \Sigma \entails \alpha 

Consistency defn 1 : There does not exists a formula \alpha such that
			\Sigma \derives \alpha and \Sigma \derives (\neg \alpha))
Consistency defn 2 : There exists an alpha which is not derivable assuming \Sigma. 

Thm: Equivalence of two notions of consistency.