Ineradicable II

Is there any sentence p such that `Definitely* p' is true? Remember we will be approximating Definitely* from a non-S5 modal system. So it is like asking what is Necessary* where that means true in every world that accessible from every world that is accessible from every world...that is accessible from the actual world. Presumably there are no such sentences p?

What about some sentence p that is true in the actual world itself? Doesn't Necessarily* define an accessibility relation (accessibility*?) which makes the world accessible* from itself?