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  "body": "\n## Summary\n\nA Mahlo cardinal is an [[inaccessible cardinal|NW4DREQ5DQ]] $\\kappa$ such that the inaccessible cardinals below $\\kappa$ form a [[stationary set|YE6WZR46RQ]] in $\\kappa$.\nSo a Mahlo cardinal has very many inaccessible cardinals below it, and it is the $\\kappa$-th inaccessible cardinal.\nThe notion is named after Paul Mahlo.\nMahlo cardinals are stronger than inaccessible cardinals, and weaker than [[weakly compact cardinals|1RHTVMH34G]].\n\n## Explanations\n\n### L1 human\n\nAn inaccessible cardinal is a size of infinity that cannot be reached from below.\nA Mahlo cardinal is an inaccessible cardinal that has inaccessible cardinals below it in a strong sense: any closed unbounded set of smaller ordinals contains one of them.\nThe first inaccessible cardinal is not Mahlo, since there is no inaccessible cardinal below it at all.\nSo Mahlo cardinals are a step up in the hierarchy of large cardinals.\n",
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