Full Idea
A statement is 'true at a possibility' if, necessarily, things would have been as the statement (actually) says they are, had the possibility obtained.
Gist of Idea
'True at a possibility' means necessarily true if what is said had obtained
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 6.6)
Book Reference
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.181
A Reaction
This is deliberately vague about what a 'possibility' is, but it is intended to be more than a property instantiation, and less than a possible world.
Related Idea
Idea 18828 If two possibilities can't share a determiner, they are incompatible [Rumfitt]