The context for personality view is the fetters:
This indicates personality view is more gross than the refined sense of self necessary to the form and formless levels (see DN 9).
(1) All three levels subject to grasping have a self. (2) The self is part of the grasping process, and keeps note of the goal, while instructing anger and desire when to act. The noble eightfold path is conditioned so it’s necessary to have a self to progress along the path:
Personality view is removed through appropriate attention and insight (seeing):
"He attends appropriately, This is stress… This is the origination of stress… This is the cessation of stress… This is the way leading to the cessation of stress. As he attends appropriately in this way, three fetters are abandoned in him: identity-view, doubt, and grasping at precepts & practices. These are called the fermentations to be abandoned by seeing.”
It’s possible to have a self but at the same time understand it’s not an ultimate reality:
"In the same way, when there is a gross acquisition of a self… it’s classified just as a gross acquisition of a self. When there is a mind-made acquisition of a self… When there is a formless acquisition of a self, it’s not classified either as a gross acquisition of a self or as a mind-made acquisition of a self. It’s classified just as a formless acquisition of a self.
“Citta, these are the world’s designations, the world’s expressions, the world’s ways of speaking, the world’s descriptions, with which the Tathagata expresses himself but without grasping to them.”