Abstract
We prove that if \({\mathbf{A}}\) is a finite algebra which satisfies a nontrivial idempotent Mal’cev condition, and if Con\({\mathbf{A}}\) contains a copy of an order polynomially complete lattice other than \({\mathbf{2}}\), \({\mathbf{M}}_{3}\), or Con\((\mathbb{Z}^{3}_{2})\), then Con\({\mathbf{A}}\) is not hereditary.
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