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  "body": "\n## Summary\n\nA finite algebra is inherently nonfinitely based when no locally finite variety that contains it is [[finitely based|YGYZAQ12MZ]].\nThis is a strong and robust way of failing to be finitely based: it passes to every finite algebra whose variety contains the given one.\nIt gives a convenient tool to show that many finite algebras, such as some finite semigroups, are not finitely based.\n\n## Explanations\n\n### L1 human\n\nSome finite algebras cannot be described by finitely many laws.\nAn inherently nonfinitely based algebra has a stronger defect.\nPut it inside any larger, still well-behaved family of algebras, and that family cannot be described by finitely many laws either.\nSo the defect cannot be repaired by enlarging the setting.\nA finite group is never like this, because the variety it generates is locally finite and finitely based.\n",
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