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arXiv · 1805.06291

Categoricity and multidimensional diagrams

Saharon Shelah·Sebastien Vasey
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Abstract

We study multidimensional diagrams in independent amalgamation in the framework of abstract elementary classes (AECs). We use them to prove the eventual categoricity conjecture for AECs, assuming a large cardinal axiom. More precisely, we show assuming the existence of a proper class of strongly compact cardinals that an AEC which has a single model of some high-enough cardinality will have a single model in any high-enough cardinal. Assuming a weak version of the generalized continuum hypothesis, we also establish the eventual categoricity conjecture for AECs with amalgamation.

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Saharon Shelah, Sebastien Vasey. 2018-05-16. Categoricity and multidimensional diagrams. https://arxiv.org/abs/1805.06291

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