Recall that the Singular Cardinals Hypothesis (SCH) says that if $\kappa$ is a singular cardinal and $2^{cf(\kappa)}<\kappa,$ then $\kappa^{cf(\kappa)}=\kappa^+.$ Clearly it has many applications in set theory, for example assuming SCH, the behavior of the power function is determined by its behavior on regular cardinals, ....

What are the main applications of SCH outside of set theory, in particular in model theory, algebra, analysis, topology, and ...(with references)?