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
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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)
Category theory
Can someone add words that clarify the distinction between model theory and category theory? Is model theory supposed to be a broadened, extended, generalized category theory? Or was historically inspired by category theory, while ditching the weighty baggage of the concept of "class" and the cardinality of class? linas 16:04, 12 Mar 2005 (UTC)
- I don't think they are related. MarSch 17:04, 19 Apr 2005 (UTC)
models of set theories
What is meant by "a model of a set theory"? Does it mean that you try to make a model in one set theory of the other set theory? MarSch 17:20, 19 Apr 2005 (UTC)
Very confused!
If "a theory is defined as a set of sentences which is consistent", then "a theory has a model if and only if it is consistent" seems very confusing. By way of illustration, "a 'set of sentences which is consistent' has a model iff it is consistent", looks very much like tautology to me. The irony of that appearing in this article is not lost on me, but this article needs a more precise and expository rewrite.
To Do List
I removed this "to do" list from the article, so I'm sticking it here.
TODO - Vaught's test. Extensions, Embeddings and Diagrams. To give a flavor, mentioning the hyperreals and/or the extension of the concepts of basis and dimension to strongly minimal theories would be good. (All of these need substantial filling out)
Josh Cherry 04:15, 21 Jun 2005 (UTC)