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Preprint Number 943

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943. Sebastien Vasey
A downward categoricity transfer for tame abstract elementary classes
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Submission date: 13 October 2015

Abstract:

We prove a downward transfer from categoricity in a successor in tame abstract elementary classes (AECs). This complements the upward transfer of Grossberg and VanDieren and improves the Hanf number in Shelah's downward transfer (provided the class is tame).

Theorem
Let K be an AEC with no maximal models and amalgamation. If K is LS(K)-weakly tame and categorical in a successor λ > LS(K)+, then K is categorical in all λ' ≥ min(λ,ℶ(2LS(K))+).

The argument uses orthogonality calculus and gives alternate proofs to both the Shelah and the Grossberg-VanDieren transfers

Mathematics Subject Classification: 03C48 (Primary), 03C45, 03C52, 03C55, 03C75, 03E55 (Secondary)

Keywords and phrases:

Full text arXiv 1510.03780: pdf, ps.


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