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arXiv · 2406.16669

The filter of interpretability types of Hobby-McKenzie varieties is prime

Bertalan Bodor·Gergő Gyenizse·Miklós Maróti·László Zádori
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Abstract

We study the Hobby-McKenzie varieties that constitute a major class investigated thoroughly in the monograph The shape of congruence lattices by Kearnes and Kiss. We obtain new characterizations of the Hobby-McKenzie varieties via compatible reflexive ternary structures. Based on our findings, we prove that in the lattice of interpretability types of varieties, the filter of the interpretability types of Hobby-McKenzie varieties is prime.

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Bertalan Bodor, Gergő Gyenizse, Miklós Maróti, László Zádori. 2026-07-24. The filter of interpretability types of Hobby-McKenzie varieties is prime. https://arxiv.org/abs/2406.16669

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