Talk: Model theory

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Is not the last sentence of the first paragraph (i.e. what can be proven given a set of axioms) closer to proof theory?

Ughh, the completness part at least needs some work. What it means for a theory to be complete is quite differnt from the completness theorem. Logicnazi 12:11, 27 Aug 2004 (UTC)

Also the statement about a theory being maximally consistant set of sentences is just wrong. Only complete theories are maximal consistant set of sentences, e.g. the theory consisting of only pure truths of predicate calculus is closed under implication but hardly maximal (otherwise we could never add axioms!!) Logicnazi 12:13, 27 Aug 2004 (UTC)

Just so no one tries to re-add the statement it is simply NOT TRUE that a complete theory fully specifies a model. The Low-Skol theorems easily prove that complete theories will have models of differnt cardinalities. Logicnazi

Maximal consistent set

Anyone fancy creating this node and providing the necessary discussion here? I'm creating a link from Consistency proof, but I have more than enough to do around proof theory. If not, I'll get around to it eventually... ---- Charles Stewart 07:48, 22 Sep 2004 (UTC)