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  "body": "\n## Summary\n\nA core model is an [[inner model|G78W36EGMB]], usually written $K$, built from fine-structural pieces like the [[constructible universe|6TF2JBTPPJ]].\nUnlike $L$, it is large enough to contain some large cardinal structure.\nIt is defined under an assumption that rules out large cardinals beyond a certain level.\nAn example of such an assumption is that there is no inner model with a [[Woodin cardinal|CMC2C1D53W]].\nUnder such an assumption the core model is close to the universe $V$, in the sense of covering properties like [[Jensen's covering theorem|RJE1W5NRE3]] for $L$.\nThe theory of the core model links large cardinals with the strength of combinatorial statements.\n\n## Explanations\n\n### L1 human\n\nThe constructible universe is a very thin and well understood world of sets.\nIf [[zero sharp|HCTNBZZQ0W]] does not exist, the constructible universe is close to the full universe, and $L$ plays the role of the core model.\nIf larger objects exist, one needs a bigger inner model that still has the good structure of $L$; this is the core model.\nIt is the largest inner model of its kind that can be built from below, and it approximates the full universe well.\nIts exact definition depends on which large cardinals are assumed not to exist.\n",
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