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 language | English |
---|---|
Pages (from-to) | 2301-2372 |
Number of pages | 72 |
Journal | Journal of the European Mathematical Society |
Volume | 26 |
Issue number | 7 |
DOIs | |
State | Published - 2024 |
Bibliographical note
Publisher Copyright:© 2024 European Mathematical Society.
Keywords
- abstract elementary classes
- categoricity
- excellence
- forking
- good frames
- multidimensional diagrams