Full Idea
Tarski's 1936 definition of logical consequence is that in any model in which the premises are true, the conclusion is true too (so that no model can make the conclusion false).
Gist of Idea
Logical consequence is when in any model in which the premises are true, the conclusion is true
Source
report of Alfred Tarski (works [1936]) by JC Beall / G Restall - Logical Consequence 3
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.6
A Reaction
So the general idea is that a logical consequence is distinguished by being unstoppable. Sounds good. But then we have monotonic and non-monotonic logics, which (I'm guessing) embody different notions of consequence.