JournalsjemsVol. 26, No. 7pp. 2301–2372

Categoricity and multidimensional diagrams

  • Saharon Shelah

    The Hebrew University of Jerusalem, Jerusalem, Israel; Rutgers, The State University of New Jersey, Piscataway, USA

  • Sebastien Vasey

    Harvard University, Cambridge, USA
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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.

Cite this article

Saharon Shelah, Sebastien Vasey, Categoricity and multidimensional diagrams. J. Eur. Math. Soc. 26 (2024), no. 7, pp. 2301–2372

DOI 10.4171/JEMS/1477