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  "body": "\n## Summary\n\nIn set theory and computability theory, **Kleene's $\\mathcal{O}$** is a canonical subset of the [[natural numbers|0MWKJ44V5A]] when regarded as ordinal notations. It contains ordinal notations for every computable ordinal, that is, ordinals below Church–Kleene ordinal, $\\omega_1^{\\text{CK}}$. Since $\\omega_1^{\\text{CK}}$ is the first ordinal not representable in a computable system of ordinal notations the elements of $\\mathcal{O}$ can be regarded as the canonical ordinal notations.\n",
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  "name": "Kleene's O",
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