proof of compactness theorem for first order logic
The theorem states that if a set of sentences of a first-order language is inconsistent, then some finite subset of it is inconsistent. Suppose is inconsistent. Then by definition , i.e. there is a formal proof of “false” using only assumptions from . Formal proofs are finite objects, so let collect all the formulas of that are used in the proof.
|Title||proof of compactness theorem for first order logic|
|Date of creation||2013-03-22 12:44:02|
|Last modified on||2013-03-22 12:44:02|
|Last modified by||CWoo (3771)|