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  "body": "\n## Summary\n\nAn ultrafilter on a [[Boolean algebra|0XADJKM699]] $B$ is a proper filter of $B$ that is maximal among proper filters.\nEquivalently, it is a filter that contains exactly one of $a$ and $\\neg a$ for every $a \\in B$.\nUltrafilters are the same as homomorphisms from $B$ onto the two-element Boolean algebra, and they are the points of the [[Stone space|ZV38HA5PAQ]] of $B$.\nFor the power set of a set $X$ one gets the [[ultrafilters|J64Y3JC0RE]] on $X$.\n\n## Explanations\n\n### L1 human\n\nAn ultrafilter picks out the elements of a Boolean algebra that count as \"true\" in one consistent way of deciding everything.\nIt decides every element: either $a$ is true or $\\neg a$ is, never both.\nIf $a$ and $b$ are true, so is \"$a$ and $b$\", and anything above a true element is true.\nIn the algebra of subsets of a finite set, every ultrafilter consists of the subsets that contain one fixed point.\n",
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