Talk:Compactness of First-Order Logic

I think this says the same as Compactness Theorem for Boolean Interpretations, but it comes at it from a different direction.

Presumably the results "consistency implies satisfiability" and "satisfiability implies consistency" are equivalent to Extended Soundness Theorem for Propositional Tableaus and Boolean Interpretations and Extended Completeness Theorem for Propositional Tableaus and Boolean Interpretations but I'm on dodgy ground with this (i.e. I don't really know what I'm doing).

Who knows how to tie all this together - like, can this page be deleted or merged with the Compactness Theorem for Boolean Interpretations?

I'm merging this into Compactness Theorem for now. While Compactness Theorem for Boolean Interpretations could be construed as a special case of these, the approach there is very different. I'm not sure whether merging them is the solution.

As a side note, the consistency/satisfiability results are the soundness and completeness theorems. The ones you've linked to are special cases for propositional calculus and have proofs with a similar approach to that of the compactness theorem for propositional calculus, so again I'm not sure whether the answer is to push them together.

Qedetc 22:03, 5 June 2011 (CDT)