Taylor is prime (Q6633829)

Recall that a Taylor variety is a variety which recognizes a non-trivial idempotent (strong) Maltsev condition. Besides, interpretability types are the blocks of quasiorders on the class of varieties. Basically, a filter \(F\) of a lattice \(\mathcal{L}\) is called prime if \(F\) is a proper subset of the lattice \(\mathcal{L}\) such that for any elements \(a, b \notin F\), \(a\vee b \notin F\). In this work, the authors consider the class of Taylor varieties and show that the filter of Taylor interpretability types is prime in \(\mathcal{L}\).