ULTRAPRODUCTS OF FINITE ALTERNATING GROUPS (Combinatorial and Descriptive Set Theory)
P.J. Ellis, Sherwood Hachtman, Scott Schneider, Simon Thomas · Institutional Repositories DataBase (IRDB) · 2008
We prove that if $\mathcal{U}$ is a nonprincipal ultrafilter over $\omega$ , then the set of normal subgroups of the ultraproduct $\prod_{\mathcal{U}}$ Alt $(n)$ is linearly ordered by inclusion.We also prove that the number of such ultraproducts up to isomorphism is either $2^{\aleph_{0}}$ or $2^{2^{\aleph_{0}}}$ , depending on whether or not $CH$ holds.