# Sh:842

• Shelah, S., & Vasey, S. Categoricity and multidimensional diagrams. Preprint. arXiv: 1805.06291
• 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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Bib entry
@article{Sh:842,
author = {Shelah, Saharon and Vasey, Sebastien},
title = {{Categoricity and multidimensional diagrams}},
note = {\href{https://arxiv.org/abs/1805.06291}{arXiv: 1805.06291}},
arxiv_number = {1805.06291},
ignore = {x}
}