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  "body": "\n## Summary\n\nThe diamond principle, written $\\diamondsuit$, is a combinatorial axiom about $\\omega_1$ introduced by Ronald Jensen.\nIt says that a sequence of guesses, one at each countable ordinal, correctly predicts every subset of $\\omega_1$ on a [[stationary set|YE6WZR46RQ]] of ordinals.\nIt holds in the [[constructible universe|6TF2JBTPPJ]], and it implies the [[continuum hypothesis|0MN2MER9WN]].\nIt is used to build objects such as Suslin trees, and the [[precise definition|J8GYFAA70H]] is given separately.\n\n## Explanations\n\n### L1 human\n\nImagine an oracle that, at each countable stage $\\alpha$, makes one guess $A_\\alpha$ about what a hidden set $A \\subseteq \\omega_1$ looks like below $\\alpha$.\nDiamond says that there is an oracle so good that, for every possible hidden set, its guesses are right at a large set of stages.\nThis is surprising, because there are $2^{\\aleph_1}$ subsets of $\\omega_1$, while each stage gets only one guess.\nSuch an oracle lets one kill every possible obstacle during a construction of length $\\omega_1$, and that is how it is used.\n",
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