{
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  "body": "\n## Summary\n\nIn set theory, a subset of a Polish space $X$ is **∞-Borel** if it can be obtained by starting with the [[open subsets|01ZQQDCERP]] of $X$, and transfinitely iterating the operations of [[complementation|0RKF1ZT5JJ]] and well-ordered [[union|0X1GSWNBN1]]. This concept is usually considered without the assumption of the [[axiom of choice|0HTGB13FE2]], which means that the ∞-Borel sets may fail to be closed under well-ordered union; see below.\n",
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