A logic in a finite language is said to be finitely presentable if it is axiomatized by finitely many finite rules. It is proved that binary non-indexed products of logics that are both finitely presentable and finitely equivalential are essentially finitely presentable. This result does not extend to binary non-indexed products of arbitrary finitely presentable logics, as shown by a counterexample. Finitely presentable logics are then exploited to introduce finitely presentable Leibniz classes, and to draw a parallel between the Leibniz and the Maltsev hierarchies.

中文翻译：

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所有逻辑的姿势 III：有限可呈现逻辑

如果有限语言中的逻辑被有限多个有限规则公理化，则称其为有限可表示的。证明了既是有限可表示的又是有限等价的逻辑的二进制非索引乘积本质上是有限可表示的。这个结果不能扩展到任意有限可表示逻辑的二进制非索引乘积，如反例所示。然后利用有限可表示的逻辑来引入有限可表示的莱布尼茨类，并在莱布尼茨和 Maltsev 层次结构之间进行平行。