Full Idea
If we have a 'fixedly' operator F, then a sentence is fixedly actually true if it is true no matter which world is designated as actual (which 'he actually won in 2008' fails to be). Maybe '□' is superficial necessity, and FA is 'deep' necessity.
Clarification
FA reads as 'Fixedly Actually'
Gist of Idea
Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual
Source
Laura Schroeter (Two-Dimensional Semantics [2010], 1.2.2)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.11
A Reaction
Gareth Evans distinguishes 'deep' from 'superficial' necessity. Humberstone and others introduced 'F'. Presumably FA is deeper because it has to pass a tougher test.