It was shown recently that epimorphisms need not be surjective in a variety $\mathsf{K}$ of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example $\mathsf{K}$. It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show that for every integer $n⩾2$, the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics.

最近表明，在许多情况下，表观同质不必是排斥的 $\mathsf{ķ}$关于Heyting代数，但到目前为止，文献中只显示了一个反例。在此，确定了这样的示例的连续体。Rieger-Nishimura格生成的变体及其包含原始反例的所有（局部有限的）子变体$\mathsf{ķ}$。众所周知，每当各种Heyting代数具有有限的深度时，它就会具有射影的同质。相反，我们表明对于每个整数$ñ⩾2$，所有宽度最多为n的Heyting代数的多样性具有非排斥的同胚性。在所谓的Kuznetsov-Gerčiu变体（即由一个生成的Heyting代数的有限线性和生成的变体）中，我们精确地描述了具有射影型同质的子变体。这产生了新的积极例子，并为所有哥德尔代数的变种的超概异性提供了另一种证明。结果解决了有关一系列中间逻辑的Beth式可定义性的自然问题。