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  "body": "\n## Summary\n\nThe axiom of constructibility, written $V = L$, says that every set is constructible, that is, every set lies in the [[constructible universe|6TF2JBTPPJ]] $L$.\nIt is consistent with [[ZF|0HE5WDQ9FJ]] when ZF is consistent, and it decides many questions that ZFC leaves open.\nIt implies the [[axiom of choice|0HTGB13FE2]] and the generalized [[continuum hypothesis|0MN2MER9WN]].\nIt is incompatible with large cardinals such as [[measurable cardinals|AKBWT323RQ]], so most set theorists do not accept it as true.\n\n## Explanations\n\n### L1 human\n\nThe constructible universe is the thinnest possible world of sets that can be built from definable pieces.\nThe axiom of constructibility says that there are no other sets at all.\nIt is like saying that every set has a description at some stage of one fixed construction.\nIn such a world many hard questions get a definite answer; for example, there are exactly $\\aleph_1$ real numbers.\n",
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