Full Idea
The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences.
Gist of Idea
The 'spheres model' was added to possible worlds, to cope with counterfactuals
Source
Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4)
Book Reference
'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.19
A Reaction
Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions.