Inherently nonfinitely based lattices

We give a general method for constructing lattices L whose equational theories are inherently nonfinitely based. This means that the equational class (that is, the variety) generated by L is locally finite and that L belongs to no locally finite finitely axiomatizable equational class. We also provide an example of a lattice which fails to be inherently nonfinitely based but whose equational theory is not finitely axiomatizable.

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