Will Adkisson : $\aleph_1$ is not a large cardinal

Posted by William Adkisson , part of the Louise Hay Logic Seminar.

At

Nov. 16, 2023, 4 p.m.

In

427 SEO

Abstract

Since $\aleph_1$ is the second infinite cardinal, it should be obvious and non-controversial that it is not in any way a large cardinal. Nonetheless, in this talk we will justify this clearly self-evident fact. We will list a number of combinatorial properties of large cardinals, including some which can consistently hold at small cardinals, and demonstrate that $\aleph_1$ does not satisfy them.