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  "body": "\n## Summary\n\nThe axiom of determinacy, written AD, says that every infinite game of natural numbers with perfect information is [[determined|QXECDPAYTN]].\nJan Mycielski and Hugo Steinhaus proposed it in 1962 as an alternative to the [[axiom of choice|0HTGB13FE2]], which it contradicts.\nIn ZF together with AD, every set of real numbers is Lebesgue measurable, has the [[Baire property|FZ7237VY65]] and has the [[perfect set property|H47ZGRR13V]].\nAD is studied in models such as $L(\\R)$, where it can hold under large cardinal hypotheses.\n\n## Explanations\n\n### L1 human\n\nPick any rule that sorts infinite sequences of natural numbers into wins and losses for the first player.\nThe axiom says that, whatever the rule, one of the two players has a strategy that always wins.\nWith the axiom of choice one can write down a strange rule for which no player has such a strategy, so AD and choice cannot both hold.\nIn exchange, AD removes the pathological sets of reals that choice creates, such as non-measurable sets.\n",
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