 In contemporary treatments of logic, logical relations between formulas of a formal language are sometimes defined in terms of relations between sets of interpretations of the language. For example, a set of formulas \(\Gamma\) might be said to imply a formula \(\alpha\) iff the set of interpretations making all members of \(\Gamma\) true is a subset of the set of interpretations making \(\alpha\) true, while \(\Gamma\) itself might be said to be satisfiable iff the set of interpretations making all its members true is non-empty.