Are you a Barbie girl, in a Barbie world? Why/why not?

In order to truly be a Barbie girl, one must exist in a Barbie world. That is to say it is necessary that you will be in a Barbie world in order to be a Barbie girl , but it is sufficient to say that if you are a Barbie girl you are in a Barbie world. I am confident of the existence of one or more Barbie girls, which means we must exist in a Barbie world. Now, am I one of said Barbie girls? No, and knowing that I am not one, but exist in their world, that knowledge frightens me.