2018/11/13 by Ulrich, Douglas
#03C55 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1811.05448
We streamline treatments of the interpretability orders \trianglelefteq^*κ of Shelah, the key new notion being that of pseudosaturation. Extending work of Malliaris and Shelah, we classify the interpretability orders on the stable theories. As a further application, we prove that for all countable theories T0, T1, if T1 is unsupersimple, then T0 \trianglelefteq^*1 T1 if and only if T0 \trianglelefteq^*ℵ1 T1. We thus deduce that simplicity is a dividing line in \trianglelefteq^*ℵ1, and that consistently, SOP2 characterizes maximality in \trianglelefteq^*ℵ1; previously these results were only known for \trianglelefteq^*1.