# Models of arithmetic with two expansions to $ACA_0$, Part 2

Models of PAWednesday, October 26, 20166:30 pmGC 4214-03

# Models of arithmetic with two expansions to $ACA_0$, Part 2

In this talk and its prequel I construct models of arithmetic with exactly two expansions to a model of $ACA_0$. Last time, we saw how to build models of arithmetic which are A-rather classless for some class A of the model. In this talk, I will use a kind of forcing argument to show how to pick this A so that the resulting model has exactly two expansions to $ACA_0$. Time permitting, I will explain the difficulties in moving from two to three.