Non Forking Good Frames without Local Character
نویسندگان
چکیده
We continue [Sh:h].II, studying stability theory for abstract elementary classes. In [Sh E46], Shelah obtained a non-forking relation for an AEC, (K, ), with LST -number at most λ, which is categorical in λ and λ and has less than 2 + models of cardinality λ, but at least one. This non-forking relation satisfies the main properties of the non-forking relation on stable first order theories. Here we improve this non-forking relation such that it satisfies the local character, too. Therefore it satisfies the main properties of the non-forking relation on superstable first order theories. Using results of [Sh:h].II, we conclude that the function λ → I(λ,K), which assigns to each cardinal λ, the number of models in K of cardinality λ, is not arbitrary.
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