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  "body": "\n## Definition\n\nLet $A$ be a finite set with at least two elements.\nAn [[operation|EJ8YJVM9BW]] $f$ on $A$ is a *Sheffer function* if the set $\\set{f}$ is [[functionally complete|TDZVCWYJ9F]].\nThat is, the [[clone|PTKR703G6A]] generated by $f$ contains every finitary operation on $A$.\n\n## Remarks\n\nExample: NAND, $x \\uparrow y = \\neg(x \\wedge y)$ on $\\set{0, 1}$, is a Sheffer function.\nCheck: $\\neg x = x \\uparrow x$ and $x \\wedge y = \\neg(x \\uparrow y)$, and $\\set{\\wedge, \\neg}$ is functionally complete.\nNon-example: $\\wedge$ on $\\set{0, 1}$ is not a Sheffer function.\nEvery operation generated by $\\wedge$ maps $(0, \\dots, 0)$ to $0$, so $\\neg$ is not generated.\nNOR, $x \\downarrow y = \\neg(x \\vee y)$, is the only other binary Sheffer function on $\\set{0, 1}$.\nA Sheffer function must have arity at least $2$, since a unary operation generates only essentially unary operations.\n",
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