Adi Jarden, Saharon Shelah. Weakening the local character

Natural Sciences / Mathematics / Algebra

Submitted on: Sep 10, 2012, 15:03:59

Description: In [Sh E46], Shelah obtained a non-forking relation for an AEC, (K,preceq), with LST-number at most lambda, which is categorical in lambda and lambda^+ and has less than 2^{lambda^+} models of cardinality lambda^{++}, but at least one. This non-forking relation satisfies the main properties of the non-forking relation on stable first order theories, but only a weak version of the local character. 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. We conclude that the function lambda to I(lambda,K), which assigns to each cardinal lambda, the number of models in K of cardinality lambda, is not arbitrary.

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