Categoricity and multidimensional diagrams

Saharon Shelah, Sebastien Vasey

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)2301-2372
Number of pages72
JournalJournal of the European Mathematical Society
Volume26
Issue number7
DOIs
StatePublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 European Mathematical Society.

Keywords

  • abstract elementary classes
  • categoricity
  • excellence
  • forking
  • good frames
  • multidimensional diagrams

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