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} }
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
- MathematicsMath. Log. Q.
- 2018
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.