Weakening the local character

Adi Jarden; Saharon Shelah

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arXiv · 1105.3674

Weakening the local character

Adi Jarden·Saharon Shelah

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Abstract

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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BibTeX RIS

Adi Jarden, Saharon Shelah. 2011-05-18. Weakening the local character. https://arxiv.org/abs/1105.3674

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