Talk:Compactness Theorem

Wikipedia claims this theorem is actually equivalent to BPIT and Gödel's Completeness Theorem. --Dfeuer (talk) 07:58, 13 December 2012 (UTC)


 * Before posting up any more proofs using this claim, it would be good to post both BPIT and GCT up on this site. As it stands, with the crucial information missing, it makes us look embarrassingly lame. It makes us look like a bunch of amateurs pretending to be clever, which is one of the main criticisms which is brought against this site. --prime mover (talk) 22:55, 13 December 2012 (UTC)


 * Sure. I can try to do some, but a lot of the set theory is over my head. It disturbs me, however, to see "this theorem depends on AoC" when in fact it only depends on BPIT, AoCC, AoDC, etc., even if I don't personally know how to prove that. --Dfeuer (talk) 22:59, 13 December 2012 (UTC)


 * I hate to say this, but if all this is over your head, should you not leave well alone? Is all you know about this what you've picked up from wikipedia? --prime mover (talk) 07:25, 14 December 2012 (UTC)

Substantial error in proof with ultraproducts
As I noted with a questionable template, $\{\uparrow(E) \mid E \in T \}$ isn't actually a filter on $\Sigma$ as claimed. I just glanced over at Wikipedia and see that rather than looking at finite sets containing individual statements, their proof considers finite sets including finite sets of statements, which makes a lot more sense. Since I don't know anything about ultraproducts yet, I don't feel comfortable trying to fix this proof, but someone really should. --Dfeuer (talk) 21:08, 24 December 2012 (UTC)