Full Idea
Under the possible worlds semantics for logical consequence, each sentence of a language is associated with a truth-set of possible worlds in which it is true, and then something is a consequence if one of these worlds verifies it.
Gist of Idea
Logical consequence is verification by a possible world within a truth-set
Source
Kit Fine (Guide to Ground [2012], 1.10)
Book Reference
'Metaphysical Grounding', ed/tr. Correia,F/Schnieder,B [CUP 2012], p.71
A Reaction
[compressed, and translated into English; see Fine for more symbolic version; I'm more at home in English]