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  "body": "\n## Summary\n\nIn set theory, a branch of mathematics, an **additively indecomposable ordinal** *α* is any [[ordinal number|0RDJK7EQYY]] that is not 0 such that for any $\\beta,\\gamma\u003c\\alpha$, we have $\\beta+\\gamma\u003c\\alpha.$ Additively indecomposable ordinals were named the *gamma numbers* by Cantor,\u003csup\u003ep.20\u003c/sup\u003e and are also called *additive principal numbers*. The class of additively indecomposable ordinals may be denoted $\\mathbb H$, from the German \"Hauptzahl\". The additively indecomposable ordinals are precisely those ordinals of the form $\\omega^\\beta$ for some ordinal $\\beta$.\n",
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