Wikipedia on Compleness Theorem : Completeness Theorem : Henkins theorem, the proof of the completeness theorem is as follows: If \models A is valid, then \lnot A does not have models. By the contrapositive of Henkins, then \lnot A is an inconsistent formula. But, by the definition of consistency, if \lnot A is inconsistent then its possible to build a proof of \vdash A. Gödels completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. It makes a close link between model theory that deals with what is true in different models, and proof theory that studies what can be formally proven in particular formal systems. My ex-colleague at PwC Prithwis-da, was likening the completeness theorem to the Godmen miracles across the ages! What an analogy, particularly helpful to explain why Godmen across ages resort to cheap tricks.
Posted on: Fri, 21 Nov 2014 17:10:51 +0000
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