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  "body": "\n## Definition\n\nLet $\\mathcal{V}$ be a [[variety of algebras|AJNZJD8442]].\nA *Siggers term* for $\\mathcal{V}$ is a $6$-ary [[term|N9M2N27END]] $s(x_1, \\dots, x_6)$ such that $\\mathcal{V}$ satisfies the [[identities|PKD440G2XW]]\n$$s(x, x, x, x, x, x) \\approx x \\quad \\text{and} \\quad s(x, y, x, z, y, z) \\approx s(y, x, z, x, z, y).$$\nThe first identity says that $s$ is [[idempotent|9FS1JFZSX4]].\n\n## Remarks\n\nExample: in the variety of semilattices, $s = x_1 \\wedge \\cdots \\wedge x_6$ is a Siggers term.\nCheck: it is idempotent, and both sides of the second identity equal $x \\wedge y \\wedge z$, by commutativity, associativity and idempotence.\nNon-example: in the variety of sets with no operations, the only terms are variables, and no variable $x_i$ is a Siggers term.\nThe two sides of the second identity differ in every place, so for $s = x_i$ it would read $x \\approx y$, $x \\approx z$ or $y \\approx z$.\nEvery Siggers term is a [[Taylor term|QEAMRNRJJD]]: substituting $z = x$, $y = x$ or $x = y$ in the second identity gives, for each place, an identity in two variables that differs in that place.\nA $4$-ary variant, an idempotent term with $s(a, r, e, a) \\approx s(r, a, r, e)$, is also used; a finite algebra has a Taylor term exactly when it has a term of this kind.\n",
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