Talk:Extended Completeness Theorem of Propositional Calculus

Should we note the relationship to the Extended Soundness Theorem of Propositional Calculus? --Cynic (talk) 00:49, 16 July 2009 (UTC)

Could do. It's joined together in Equivalence of Logical Consequence and Logical Implication, but I suppose there's nothing to stop us cross-referencing each to each other. --Matt Westwood 07:54, 16 July 2009 (UTC)

New favorite mathematical statement, btw: $\dashv\vdash \iff =\!\!\! | \!\! \models$

Correct me if that's bad syntax. --Cynic (talk) 22:26, 16 July 2009 (UTC)

Delightful, isn't it?

The trouble is, it's tricky to distinguish between $\iff$ when used as a logical connective, and $\iff$ as used as a metasymbol ...

My brain hurts. I'm looking forward to getting all this logic out of the way so I can move on to properly axiomatising set theory. Maybe someone else will turn up and sort out this mess. --Matt Westwood 22:48, 16 July 2009 (UTC)