• 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. 
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On the universality of the nonstationary ideal

TLDR
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.