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Tameness from two successive good frames

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Abstract

We show, assuming a mild set-theoretic hypothesis, that if an abstract elementary class (AEC) has a superstable-like forking notion for models of cardinality λ and a superstable-like forking notion for models of cardinality λ+, then orbital types over models of cardinality λ+ are determined by their restrictions to submodels of cardinality λ. By a superstable-like forking notion, we mean here a good frame, a central concept of Shelah’s book on AECs.

It is known that locality of orbital types together with the existence of a superstable-like notion for models of cardinality λ implies the existence of a superstable-like notion for models of cardinality λ+, and here we prove the converse. An immediate consequence is that forking in λ+ can be described in terms of forking in λ.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Sebastien Vasey

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  1. Sebastien Vasey
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Correspondence to Sebastien Vasey.

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Vasey, S. Tameness from two successive good frames. Isr. J. Math. 235, 465–500 (2020). https://doi.org/10.1007/s11856-020-1965-4

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  • DOI: https://doi.org/10.1007/s11856-020-1965-4

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