Probably important to point this out: private property is not personal property.

E.g. An apartment building rented to tenants is the landlords private property. They have exclusive rights to the decisions, especially economic ones, regarding the building and the profits of the rent.

A car, book, house, pizza, are all your personal property so long as you don't owe a lender anything for them.

So no private property might look like:

The people who live in an apartment building own the building collectively and have the full right therein, but the individual units are each their own personal property.