 Theorem. Suppose that \(\prec\) is a strict order over \(W\). Define the consequence relation \(\dproves\) by setting \(\alpha \dproves \beta\) iff \(\beta\) is true in all the \(\alpha\)-minimal worlds. Then, \(\dproves\) satisfies KLM1-6. If \(\prec\) is total, KLM7 is also satisfied. Conversely, suppose that the consequence relation \(\dproves\) satisfies KLM1–6. Then, there is a strict order \(\prec\), such that \(\alpha \dproves \beta\) iff \(\beta\) is true in all the \(\alpha\)-minimal worlds. If KLM7 is also satisfied, then the order can be chosen to be total.