Sh:842
- Shelah, S., & Vasey, S. (2024). Categoricity and multidimensional diagrams. J. Eur. Math. Soc. (JEMS), 26(7), 2301–2372. arXiv: 1805.06291 DOI: 10.4171/jems/1477 MR: 4756567
-
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) published version (72p)
Bib entry
@article{Sh:842,
author = {Shelah, Saharon and Vasey, Sebastien},
title = {{Categoricity and multidimensional diagrams}},
journal = {J. Eur. Math. Soc. (JEMS)},
fjournal = {Journal of the European Mathematical Society (JEMS)},
volume = {26},
number = {7},
year = {2024},
pages = {2301--2372},
issn = {1435-9855},
mrnumber = {4756567},
mrclass = {03C48 (03C45 03C52 03C55 03C75 03E05 03E55)},
doi = {10.4171/jems/1477},
note = {\href{https://arxiv.org/abs/1805.06291}{arXiv: 1805.06291}},
arxiv_number = {1805.06291}
}