## The McKinsey axiom is not canonical.(English)Zbl 0744.03019

Let $$L$$ be a logic, and $${\mathcal F}_ L$$ a canonical frame which invalidates every nontheorem of $$L$$. If, in addition, each $$L$$-theorem is valid in $${\mathcal F}_ L$$, then $$L$$ is said to be canonical. The logic $$KM$$ is the smallest normal modal logic that includes the McKinsey axiom $$\square\diamondsuit\varphi\to\diamondsuit\square\varphi$$. The paper contains the proof that this axiom is not valid in the canonical frame for $$KM$$.

### MSC:

 03B45 Modal logic (including the logic of norms)
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### References:

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