{
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  "body": "\n## Summary\n\nIn [[combinatorics|0JKW7W7XFR]], a **Helly family** of order $k$ is a family of [[sets|0BSJ7RQ9BW]] in which every minimal *subfamily with an empty [[intersection|0ZNMMA9TF5]]* has $k$ or fewer sets in it. Equivalently, every finite subfamily such that every $k$-fold intersection is non-empty has non-empty total intersection. The **$k$-Helly property** is the property of being a Helly family of order $k$.\n",
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