 The contemporary model-theoretic definition of logical consequence traces back to Tarski (1936). It builds on the definition of truth in a model given by Tarski in (1935). Tarski defines a true sentence in a model recursively, by giving truth (or satisfaction) conditions on the logical vocabulary. A conjunction, for example, is true in a model if and only if both conjuncts are true in that model. A universally quantified sentence \(\forall xFx\) is true in a model if and only if each instance is true in the model. (Or, on the Tarskian account of satisfaction, if and only if the open sentence \(Fx\) is satisfied by every object in the domain of the model. For detail on how this is accomplished, see the entry on  Tarski’s truth definitions.)  Now we can define logical consequence as preservation of truth over models: an argument is valid if in any model in which the premises are true (or in any interpretation of the premises according to which they are true), the conclusion is true too.