McKinsey公理 在弱传递框架类上有局部一阶对应。在框架类上，Mckinsey公理全局对应于Lemmon所提出的一阶公式。模态公式在弱传递模态逻辑上是典范的。模态逻辑具有有穷模型性。对于任意一个自然数，模态逻辑都具有有穷模型性，进而也都是可判定的。这些模态逻辑构成了区间中的一条无限下降链。
The McKinsey axiom has a local first-order correspondent on the class of all weakly transitive frames . It globally corresponds to Lemmon’s condition on . The formula is canonical over the weakly transitive modal logic . The modal logic has the finite model property. The modal logics () form an infinite descending chain in the interval and each of them has the finite model property. Thus all the modal logics and () are decidable.
