Full Idea
The logic of real possibilities and necessities is just S5. This is because the accessibility relation for real possibilities links possible worlds of the same natural kind, which is an equivalence class.
Gist of Idea
Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind
Source
Brian Ellis (Scientific Essentialism [2001], 7.06)
Book Reference
Ellis,Brian: 'Scientific Essentialism' [CUP 2007], p.242
A Reaction
Most people, except Nathan Salmon, agree with this. With full accessibility, you seem to take epistemological problems out of the system, and just focus on reality.