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.
• Version 2024-02-25_2 (76p)

@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}
}