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  "body": "\n## Statement\n\nLet $FS(\\{x_i\\}_{i = 1}^n)$ denote the set of all finite sums of elements of $\\{x_i\\}_{i = 1}^n$. Let $C$ be a (possibly infinite) coloring of the positive integers, and let $n$ be an arbitrary positive integer. There exists $\\{x_i\\}_{i = 1}^n$ such that at least one of the following 3 conditions holds.\n\n\\1) $FS(\\{x_i\\}_{i = 1}^n)$ is a monochromatic set.\n\n\\2) $FS(\\{x_i\\}_{i = 1}^n)$ is a rainbow set.\n\n\\3) For any $B \\subseteq [1,n]$, the color of $\\sum_{i \\in B}x_i$ is determined solely by $\\min(B)$.\n",
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  "name": "Canonical Folkman Theorem",
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