• Corpus ID: 210116439

# On a strengthening of J\'onssonness for $\aleph_\omega$.

@article{Eskew2020OnAS,
title={On a strengthening of J\'onssonness for \$\aleph\_\omega\$.},
author={Monroe Eskew},
journal={arXiv: Logic},
year={2020}
}
• Monroe Eskew
• Published 13 October 2019
• Mathematics
• arXiv: Logic
We discuss a system of strengthenings of "$\aleph_\omega$ is J\'onsson" indexed by real numbers, and identify a strongest one. We give a proof of a theorem of Silver and show that there is a barrier to weakening its hypothesis.

## References

On the universality of the nonstationary ideal
This work provides a characterization of supercompactness in terms of short extender and canonical projections of NS, without any reference to the strength of the extenders; as a corollary, NS can consistently fail to canonically project to arbitrarily strong short extenders.